LMFDB - Embedded newform 315.2.t.b.101.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [315,2,Mod(101,315)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(315, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([1, 0, 1]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("315.101");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 315 = 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	315.t (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$2.51528766367$
Analytic rank:	$0$
Dimension:	$30$
Relative dimension:	$15$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			101.3
Character	$\chi$	$=$	315.101
Dual form			315.2.t.b.131.13

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.82056i q^{2} +(1.12156 - 1.31989i) q^{3} -1.31444 q^{4} +(0.500000 - 0.866025i) q^{5} +(-2.40293 - 2.04187i) q^{6} +(-1.92980 + 1.80994i) q^{7} -1.24811i q^{8} +(-0.484202 - 2.96067i) q^{9} +O(q^{10})$	\(q-1.82056i q^{2} +(1.12156 - 1.31989i) q^{3} -1.31444 q^{4} +(0.500000 - 0.866025i) q^{5} +(-2.40293 - 2.04187i) q^{6} +(-1.92980 + 1.80994i) q^{7} -1.24811i q^{8} +(-0.484202 - 2.96067i) q^{9} +(-1.57665 - 0.910280i) q^{10} +(0.241650 - 0.139517i) q^{11} +(-1.47422 + 1.73491i) q^{12} +(-2.20610 + 1.27369i) q^{13} +(3.29511 + 3.51331i) q^{14} +(-0.582275 - 1.63124i) q^{15} -4.90113 q^{16} +(1.04150 - 1.80393i) q^{17} +(-5.39007 + 0.881518i) q^{18} +(6.77701 - 3.91271i) q^{19} +(-0.657218 + 1.13833i) q^{20} +(0.224535 + 4.57707i) q^{21} +(-0.253998 - 0.439938i) q^{22} +(1.55606 + 0.898389i) q^{23} +(-1.64736 - 1.39983i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(2.31883 + 4.01634i) q^{26} +(-4.45081 - 2.68148i) q^{27} +(2.53659 - 2.37905i) q^{28} +(6.88216 + 3.97342i) q^{29} +(-2.96978 + 1.06007i) q^{30} +8.28025i q^{31} +6.42658i q^{32} +(0.0868790 - 0.475427i) q^{33} +(-3.28416 - 1.89611i) q^{34} +(0.602558 + 2.57622i) q^{35} +(0.636452 + 3.89161i) q^{36} +(-0.516727 - 0.894997i) q^{37} +(-7.12332 - 12.3380i) q^{38} +(-0.793147 + 4.34033i) q^{39} +(-1.08090 - 0.624055i) q^{40} +(2.77745 + 4.81068i) q^{41} +(8.33283 - 0.408779i) q^{42} +(-1.32175 + 2.28933i) q^{43} +(-0.317633 + 0.183386i) q^{44} +(-2.80611 - 1.06100i) q^{45} +(1.63557 - 2.83289i) q^{46} +8.97348 q^{47} +(-5.49692 + 6.46894i) q^{48} +(0.448220 - 6.98564i) q^{49} +(-1.57665 + 0.910280i) q^{50} +(-1.21288 - 3.39787i) q^{51} +(2.89978 - 1.67419i) q^{52} +(-6.17152 - 3.56313i) q^{53} +(-4.88179 + 8.10296i) q^{54} -0.279033i q^{55} +(2.25901 + 2.40860i) q^{56} +(2.43650 - 13.3332i) q^{57} +(7.23384 - 12.5294i) q^{58} +2.15780 q^{59} +(0.765363 + 2.14417i) q^{60} +3.40467i q^{61} +15.0747 q^{62} +(6.29305 + 4.83710i) q^{63} +1.89770 q^{64} +2.54739i q^{65} +(-0.865543 - 0.158168i) q^{66} -11.9688 q^{67} +(-1.36898 + 2.37115i) q^{68} +(2.93098 - 1.04622i) q^{69} +(4.69017 - 1.09699i) q^{70} +4.67203i q^{71} +(-3.69524 + 0.604337i) q^{72} +(-1.03587 - 0.598059i) q^{73} +(-1.62939 + 0.940732i) q^{74} +(-1.70384 - 0.311357i) q^{75} +(-8.90795 + 5.14301i) q^{76} +(-0.213818 + 0.706611i) q^{77} +(7.90182 + 1.44397i) q^{78} +11.2774 q^{79} +(-2.45057 + 4.24450i) q^{80} +(-8.53110 + 2.86712i) q^{81} +(8.75813 - 5.05651i) q^{82} +(7.70913 - 13.3526i) q^{83} +(-0.295137 - 6.01627i) q^{84} +(-1.04150 - 1.80393i) q^{85} +(4.16786 + 2.40632i) q^{86} +(12.9632 - 4.62724i) q^{87} +(-0.174132 - 0.301606i) q^{88} +(-2.67584 - 4.63470i) q^{89} +(-1.93162 + 5.10870i) q^{90} +(1.95201 - 6.45088i) q^{91} +(-2.04533 - 1.18087i) q^{92} +(10.9290 + 9.28681i) q^{93} -16.3368i q^{94} -7.82542i q^{95} +(8.48235 + 7.20780i) q^{96} +(7.63783 + 4.40971i) q^{97} +(-12.7178 - 0.816012i) q^{98} +(-0.530069 - 0.647891i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q + 4 q^{3} - 30 q^{4} + 15 q^{5} - q^{6} - 3 q^{7} - 2 q^{9}+O(q^{10}) $ 30 * q + 4 * q^3 - 30 * q^4 + 15 * q^5 - q^6 - 3 * q^7 - 2 * q^9	$ 30 q + 4 q^{3} - 30 q^{4} + 15 q^{5} - q^{6} - 3 q^{7} - 2 q^{9} + 3 q^{10} + 9 q^{11} + 15 q^{12} - 12 q^{13} - 27 q^{14} - q^{15} + 42 q^{16} - 3 q^{17} - 4 q^{18} - 15 q^{20} + 4 q^{21} + 15 q^{22} + q^{24} - 15 q^{25} + 24 q^{26} - 5 q^{27} + 27 q^{28} - 2 q^{30} - 25 q^{33} + 48 q^{34} - 6 q^{35} + 21 q^{36} - 3 q^{37} - 30 q^{38} - 3 q^{39} + 3 q^{40} - 18 q^{41} - 16 q^{42} + 12 q^{43} + 15 q^{44} - 7 q^{45} + 9 q^{46} - 60 q^{47} - 40 q^{48} - 15 q^{49} + 3 q^{50} - 48 q^{51} - 33 q^{52} - 30 q^{53} + 35 q^{54} + 42 q^{56} - 21 q^{57} + 30 q^{59} + 33 q^{60} + 12 q^{62} - 47 q^{63} - 138 q^{64} + 100 q^{66} + 12 q^{67} - 21 q^{68} + 32 q^{69} - 18 q^{70} + 85 q^{72} + 6 q^{73} + 54 q^{74} - 5 q^{75} - 54 q^{76} - 9 q^{77} - 18 q^{78} + 24 q^{79} + 21 q^{80} - 14 q^{81} + 6 q^{82} - 6 q^{83} - 9 q^{84} + 3 q^{85} - 60 q^{86} - 16 q^{87} - 48 q^{88} - 3 q^{89} + 22 q^{90} + 15 q^{91} - 3 q^{92} + 69 q^{93} - 48 q^{96} + 36 q^{97} + 24 q^{98} - q^{99}+O(q^{100}) $ 30 * q + 4 * q^3 - 30 * q^4 + 15 * q^5 - q^6 - 3 * q^7 - 2 * q^9 + 3 * q^10 + 9 * q^11 + 15 * q^12 - 12 * q^13 - 27 * q^14 - q^15 + 42 * q^16 - 3 * q^17 - 4 * q^18 - 15 * q^20 + 4 * q^21 + 15 * q^22 + q^24 - 15 * q^25 + 24 * q^26 - 5 * q^27 + 27 * q^28 - 2 * q^30 - 25 * q^33 + 48 * q^34 - 6 * q^35 + 21 * q^36 - 3 * q^37 - 30 * q^38 - 3 * q^39 + 3 * q^40 - 18 * q^41 - 16 * q^42 + 12 * q^43 + 15 * q^44 - 7 * q^45 + 9 * q^46 - 60 * q^47 - 40 * q^48 - 15 * q^49 + 3 * q^50 - 48 * q^51 - 33 * q^52 - 30 * q^53 + 35 * q^54 + 42 * q^56 - 21 * q^57 + 30 * q^59 + 33 * q^60 + 12 * q^62 - 47 * q^63 - 138 * q^64 + 100 * q^66 + 12 * q^67 - 21 * q^68 + 32 * q^69 - 18 * q^70 + 85 * q^72 + 6 * q^73 + 54 * q^74 - 5 * q^75 - 54 * q^76 - 9 * q^77 - 18 * q^78 + 24 * q^79 + 21 * q^80 - 14 * q^81 + 6 * q^82 - 6 * q^83 - 9 * q^84 + 3 * q^85 - 60 * q^86 - 16 * q^87 - 48 * q^88 - 3 * q^89 + 22 * q^90 + 15 * q^91 - 3 * q^92 + 69 * q^93 - 48 * q^96 + 36 * q^97 + 24 * q^98 - q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/315\mathbb{Z}\right)^\times$.

$n$	$127$	$136$	$281$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{6}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		−	1.82056i		−	1.28733i	−0.765307	−	0.643665i	$-0.777413\pi$
$2$		−	1.82056i		−	1.28733i	0.765307	−	0.643665i	$-0.222587\pi$
$3$	1.12156	−	1.31989i	0.647534	−	0.762037i
$3$	1.12156	−	1.31989i	0.647534	−	0.762037i
$4$	−1.31444			−0.657218
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$6$	−2.40293	−	2.04187i	−0.980993	−	0.833589i
$7$	−1.92980	+	1.80994i	−0.729394	+	0.684094i
$7$	−1.92980	+	1.80994i	−0.729394	+	0.684094i
$8$		−	1.24811i		−	0.441274i
$9$	−0.484202	−	2.96067i	−0.161401	−	0.986889i
$10$	−1.57665	−	0.910280i	−0.498581	−	0.287856i
$11$	0.241650	−	0.139517i	0.0728602	−	0.0420658i	−0.463127	−	0.886292i	$-0.653273\pi$
$11$	0.241650	−	0.139517i	0.0728602	−	0.0420658i	0.535988	+	0.844226i	$0.319939\pi$
$12$	−1.47422	+	1.73491i	−0.425571	+	0.500824i
$13$	−2.20610	+	1.27369i	−0.611862	+	0.353259i	−0.773694	−	0.633560i	$-0.781593\pi$
$13$	−2.20610	+	1.27369i	−0.611862	+	0.353259i	0.161832	+	0.986818i	$0.448260\pi$
$14$	3.29511	+	3.51331i	0.880654	+	0.938971i
$15$	−0.582275	−	1.63124i	−0.150343	−	0.421185i
$16$	−4.90113			−1.22528
$17$	1.04150	−	1.80393i	0.252600	−	0.437517i	−0.711641	−	0.702544i	$-0.752048\pi$
$17$	1.04150	−	1.80393i	0.252600	−	0.437517i	0.964241	+	0.265027i	$0.0853809\pi$
$18$	−5.39007	+	0.881518i	−1.27045	+	0.207776i
$19$	6.77701	−	3.91271i	1.55475	−	0.897637i	0.557009	−	0.830506i	$-0.311949\pi$
$19$	6.77701	−	3.91271i	1.55475	−	0.897637i	0.997744	−	0.0671307i	$-0.0213844\pi$
$20$	−0.657218	+	1.13833i	−0.146958	+	0.254539i
$21$	0.224535	+	4.57707i	0.0489975	+	0.998799i
$22$	−0.253998	−	0.439938i	−0.0541526	−	0.0937951i
$23$	1.55606	+	0.898389i	0.324460	+	0.187327i	0.653379	−	0.757031i	$-0.273351\pi$
$23$	1.55606	+	0.898389i	0.324460	+	0.187327i	−0.328919	+	0.944358i	$0.606684\pi$
$24$	−1.64736	−	1.39983i	−0.336267	−	0.285739i
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$	2.31883	+	4.01634i	0.454761	+	0.787669i
$27$	−4.45081	−	2.68148i	−0.856558	−	0.516051i
$28$	2.53659	−	2.37905i	0.479371	−	0.449599i
$29$	6.88216	+	3.97342i	1.27799	+	0.737845i	0.976478	−	0.215619i	$-0.0691768\pi$
$29$	6.88216	+	3.97342i	1.27799	+	0.737845i	0.301508	+	0.953464i	$0.402510\pi$
$30$	−2.96978	+	1.06007i	−0.542204	+	0.193541i
$31$			8.28025i			1.48718i	0.668637	+	0.743589i	$0.266878\pi$
$31$			8.28025i			1.48718i	−0.668637	+	0.743589i	$0.733122\pi$
$32$			6.42658i			1.13607i
$33$	0.0868790	−	0.475427i	0.0151237	−	0.0827612i
$34$	−3.28416	−	1.89611i	−0.563228	−	0.325180i
$35$	0.602558	+	2.57622i	0.101851	+	0.435461i
$36$	0.636452	+	3.89161i	0.106075	+	0.648601i
$37$	−0.516727	−	0.894997i	−0.0849493	−	0.147137i	0.820420	−	0.571761i	$-0.193740\pi$
$37$	−0.516727	−	0.894997i	−0.0849493	−	0.147137i	−0.905370	+	0.424624i	$0.860406\pi$
$38$	−7.12332	−	12.3380i	−1.15556	−	2.00148i
$39$	−0.793147	+	4.34033i	−0.127005	+	0.695009i
$40$	−1.08090	−	0.624055i	−0.170905	−	0.0986718i
$41$	2.77745	+	4.81068i	0.433764	+	0.751302i	0.997194	−	0.0748621i	$-0.0238517\pi$
$41$	2.77745	+	4.81068i	0.433764	+	0.751302i	−0.563429	+	0.826164i	$0.690518\pi$
$42$	8.33283	−	0.408779i	1.28578	−	0.0630760i
$43$	−1.32175	+	2.28933i	−0.201564	+	0.349120i	−0.949033	−	0.315178i	$-0.897936\pi$
$43$	−1.32175	+	2.28933i	−0.201564	+	0.349120i	0.747468	+	0.664297i	$0.231269\pi$
$44$	−0.317633	+	0.183386i	−0.0478850	+	0.0276464i
$45$	−2.80611	−	1.06100i	−0.418311	−	0.158165i
$46$	1.63557	−	2.83289i	0.241152	−	0.417687i
$47$	8.97348			1.30892			0.654458	−	0.756098i	$-0.272897\pi$
$47$	8.97348			1.30892			0.654458	+	0.756098i	$0.272897\pi$
$48$	−5.49692	+	6.46894i	−0.793412	+	0.933711i
$49$	0.448220	−	6.98564i	0.0640315	−	0.997948i
$50$	−1.57665	+	0.910280i	−0.222972	+	0.128733i
$51$	−1.21288	−	3.39787i	−0.169837	−	0.475798i
$52$	2.89978	−	1.67419i	0.402127	−	0.232168i
$53$	−6.17152	−	3.56313i	−0.847723	−	0.489433i	0.0121589	−	0.999926i	$-0.496130\pi$
$53$	−6.17152	−	3.56313i	−0.847723	−	0.489433i	−0.859882	+	0.510493i	$0.829463\pi$
$54$	−4.88179	+	8.10296i	−0.664327	+	1.10267i
$55$		−	0.279033i		−	0.0376248i
$56$	2.25901	+	2.40860i	0.301873	+	0.321862i
$57$	2.43650	−	13.3332i	0.322722	−	1.76603i
$58$	7.23384	−	12.5294i	0.949850	−	1.64519i
$59$	2.15780			0.280922			0.140461	−	0.990086i	$-0.455142\pi$
$59$	2.15780			0.280922			0.140461	+	0.990086i	$0.455142\pi$
$60$	0.765363	+	2.14417i	0.0988079	+	0.276811i
$61$			3.40467i			0.435923i	0.975957	+	0.217961i	$0.0699407\pi$
$61$			3.40467i			0.435923i	−0.975957	+	0.217961i	$0.930059\pi$
$62$	15.0747			1.91449
$63$	6.29305	+	4.83710i	0.792849	+	0.609418i
$64$	1.89770			0.237213
$65$			2.54739i			0.315964i
$66$	−0.865543	−	0.158168i	−0.106541	−	0.0194692i
$67$	−11.9688			−1.46223			−0.731113	−	0.682257i	$-0.760999\pi$
$67$	−11.9688			−1.46223			−0.731113	+	0.682257i	$0.760999\pi$
$68$	−1.36898	+	2.37115i	−0.166014	+	0.287544i
$69$	2.93098	−	1.04622i	0.352849	−	0.125950i
$70$	4.69017	−	1.09699i	0.560582	−	0.131116i
$71$			4.67203i			0.554467i	0.960803	+	0.277234i	$0.0894176\pi$
$71$			4.67203i			0.554467i	−0.960803	+	0.277234i	$0.910582\pi$
$72$	−3.69524	+	0.604337i	−0.435488	+	0.0712218i
$73$	−1.03587	−	0.598059i	−0.121239	−	0.0699975i	0.438154	−	0.898900i	$-0.355632\pi$
$73$	−1.03587	−	0.598059i	−0.121239	−	0.0699975i	−0.559393	+	0.828902i	$0.688966\pi$
$74$	−1.62939	+	0.940732i	−0.189413	+	0.109358i
$75$	−1.70384	−	0.311357i	−0.196742	−	0.0359524i
$76$	−8.90795	+	5.14301i	−1.02181	+	0.589943i
$77$	−0.213818	+	0.706611i	−0.0243668	+	0.0805258i
$78$	7.90182	+	1.44397i	0.894705	+	0.163497i
$79$	11.2774			1.26881			0.634403	−	0.773003i	$-0.281246\pi$
$79$	11.2774			1.26881			0.634403	+	0.773003i	$0.281246\pi$
$80$	−2.45057	+	4.24450i	−0.273982	+	0.474550i
$81$	−8.53110	+	2.86712i	−0.947900	+	0.318569i
$82$	8.75813	−	5.05651i	0.967174	−	0.558398i
$83$	7.70913	−	13.3526i	0.846187	−	1.46564i	−0.0384001	−	0.999262i	$-0.512226\pi$
$83$	7.70913	−	13.3526i	0.846187	−	1.46564i	0.884587	−	0.466376i	$-0.154441\pi$
$84$	−0.295137	−	6.01627i	−0.0322021	−	0.656429i
$85$	−1.04150	−	1.80393i	−0.112966	−	0.195663i
$86$	4.16786	+	2.40632i	0.449432	+	0.259480i
$87$	12.9632	−	4.62724i	1.38980	−	0.496093i
$88$	−0.174132	−	0.301606i	−0.0185625	−	0.0321513i
$89$	−2.67584	−	4.63470i	−0.283639	−	0.491277i	0.688639	−	0.725104i	$-0.258208\pi$
$89$	−2.67584	−	4.63470i	−0.283639	−	0.491277i	−0.972278	+	0.233827i	$0.924875\pi$
$90$	−1.93162	+	5.10870i	−0.203610	+	0.538504i
$91$	1.95201	−	6.45088i	0.204627	−	0.676236i
$92$	−2.04533	−	1.18087i	−0.213241	−	0.123115i
$93$	10.9290	+	9.28681i	1.13328	+	0.962997i
$94$		−	16.3368i		−	1.68501i
$95$		−	7.82542i		−	0.802871i
$96$	8.48235	+	7.20780i	0.865727	+	0.735643i
$97$	7.63783	+	4.40971i	0.775505	+	0.447738i	0.834835	−	0.550501i	$-0.185563\pi$
$97$	7.63783	+	4.40971i	0.775505	+	0.447738i	−0.0593302	+	0.998238i	$0.518896\pi$
$98$	−12.7178	−	0.816012i	−1.28469	−	0.0824296i
$99$	−0.530069	−	0.647891i	−0.0532740	−	0.0651155i
$100$	0.657218	+	1.13833i	0.0657218	+	0.113833i
$101$	−9.13510	−	15.8225i	−0.908977	−	1.57439i	−0.815488	−	0.578774i	$-0.803531\pi$
$101$	−9.13510	−	15.8225i	−0.908977	−	1.57439i	−0.0934886	−	0.995620i	$-0.529802\pi$
$102$	−6.18603	+	2.20811i	−0.612508	+	0.218636i
$103$	11.4173	+	6.59177i	1.12498	+	0.649506i	0.942667	−	0.333735i	$-0.108309\pi$
$103$	11.4173	+	6.59177i	1.12498	+	0.649506i	0.182311	+	0.983241i	$0.441642\pi$
$104$	1.58971	+	2.75346i	0.155884	+	0.269999i
$105$	4.07613	+	2.09408i	0.397789	+	0.204362i
$106$	−6.48688	+	11.2356i	−0.630062	+	1.09130i
$107$	−6.07964	+	3.51008i	−0.587741	+	0.339332i	−0.764204	−	0.644975i	$-0.776868\pi$
$107$	−6.07964	+	3.51008i	−0.587741	+	0.339332i	0.176463	+	0.984307i	$0.443534\pi$
$108$	5.85030	+	3.52463i	0.562945	+	0.339158i
$109$	−5.11031	+	8.85131i	−0.489479	+	0.847802i	−0.999927	−	0.0121066i	$-0.996146\pi$
$109$	−5.11031	+	8.85131i	−0.489479	+	0.847802i	0.510448	+	0.859909i	$0.329480\pi$
$110$	−0.507997			−0.0484356
$111$	−1.76084	−	0.321773i	−0.167131	−	0.0305413i
$112$	9.45818	−	8.87076i	0.893714	−	0.838208i
$113$	−9.97275	+	5.75777i	−0.938157	+	0.541645i	−0.889382	−	0.457165i	$-0.848865\pi$
$113$	−9.97275	+	5.75777i	−0.938157	+	0.541645i	−0.0487750	+	0.998810i	$0.515532\pi$
$114$	−24.2739	−	4.43579i	−2.27346	−	0.415450i
$115$	1.55606	−	0.898389i	0.145103	−	0.0837752i
$116$	−9.04616	−	5.22280i	−0.839915	−	0.484925i
$117$	4.83918	+	5.91481i	0.447382	+	0.546824i
$118$		−	3.92841i		−	0.361640i
$119$	1.25513	+	5.36626i	0.115057	+	0.491925i
$120$	−2.03597	+	0.726743i	−0.185858	+	0.0663423i
$121$	−5.46107	+	9.45885i	−0.496461	+	0.859896i
$122$	6.19840			0.561176
$123$	9.46463	+	1.72956i	0.853397	+	0.155949i
$124$		−	10.8839i		−	0.977400i
$125$	−1.00000			−0.0894427
$126$	8.80624	−	11.4569i	0.784522	−	1.02066i
$127$	−14.5854			−1.29424			−0.647121	−	0.762387i	$-0.724027\pi$
$127$	−14.5854			−1.29424			−0.647121	+	0.762387i	$0.724027\pi$
$128$			9.39827i			0.830698i
$129$	1.53924	+	4.31218i	0.135522	+	0.379666i
$130$	4.63767			0.406750
$131$	−1.65557	+	2.86753i	−0.144648	+	0.250537i	−0.929241	−	0.369473i	$-0.879538\pi$
$131$	−1.65557	+	2.86753i	−0.144648	+	0.250537i	0.784594	+	0.620010i	$0.212871\pi$
$132$	−0.114197	+	0.624918i	−0.00993956	+	0.0543921i
$133$	−5.99647	+	19.8167i	−0.519960	+	1.71833i
$134$			21.7900i			1.88237i
$135$	−4.54763	+	2.51377i	−0.391398	+	0.216351i
$136$	−2.25150	−	1.29990i	−0.193065	−	0.111466i
$137$	−8.30095	+	4.79255i	−0.709198	+	0.409456i	−0.810764	−	0.585373i	$-0.800948\pi$
$137$	−8.30095	+	4.79255i	−0.709198	+	0.409456i	0.101566	+	0.994829i	$0.467615\pi$
$138$	−1.90470	−	5.33603i	−0.162139	−	0.454233i
$139$	1.53543	−	0.886482i	0.130234	−	0.0751904i	−0.433468	−	0.901169i	$-0.642710\pi$
$139$	1.53543	−	0.886482i	0.130234	−	0.0751904i	0.563701	+	0.825979i	$0.309377\pi$
$140$	−0.792024	−	3.38628i	−0.0669382	−	0.286193i
$141$	10.0643	−	11.8440i	0.847568	−	0.997443i
$142$	8.50570			0.713782
$143$	−0.355403	+	0.615575i	−0.0297203	+	0.0514770i
$144$	2.37314	+	14.5106i	0.197761	+	1.20922i
$145$	6.88216	−	3.97342i	0.571532	−	0.329974i
$146$	−1.08880	+	1.88586i	−0.0901099	+	0.156075i
$147$	−8.71754	−	8.42642i	−0.719011	−	0.694999i
$148$	0.679204	+	1.17642i	0.0558302	+	0.0967008i
$149$	−9.81185	−	5.66487i	−0.803818	−	0.464084i	0.0409865	−	0.999160i	$-0.486950\pi$
$149$	−9.81185	−	5.66487i	−0.803818	−	0.464084i	−0.844804	+	0.535075i	$0.820283\pi$
$150$	−0.566844	+	3.10193i	−0.0462826	+	0.253272i
$151$	−9.03557	−	15.6501i	−0.735304	−	1.27358i	−0.954590	−	0.297923i	$-0.903706\pi$
$151$	−9.03557	−	15.6501i	−0.735304	−	1.27358i	0.219286	−	0.975661i	$-0.429627\pi$
$152$	−4.88349	−	8.45846i	−0.396104	−	0.686072i
$153$	−5.84512	−	2.21006i	−0.472550	−	0.178673i
$154$	1.28643	+	0.389268i	0.103663	+	0.0313681i
$155$	7.17091	+	4.14013i	0.575981	+	0.332543i
$156$	1.04254	−	5.70508i	0.0834700	−	0.456772i
$157$			20.5503i			1.64009i	0.572296	+	0.820047i	$0.306053\pi$
$157$			20.5503i			1.64009i	−0.572296	+	0.820047i	$0.693947\pi$
$158$		−	20.5312i		−	1.63337i
$159$	−11.6247	+	4.14944i	−0.921895	+	0.329072i
$160$	5.56558	+	3.21329i	0.439998	+	0.254033i
$161$	−4.62890	+	1.08266i	−0.364808	+	0.0853258i
$162$	5.21976	+	15.5314i	0.410103	+	1.22026i
$163$	−0.386774	−	0.669912i	−0.0302945	−	0.0524716i	0.850481	−	0.526006i	$-0.176311\pi$
$163$	−0.386774	−	0.669912i	−0.0302945	−	0.0524716i	−0.880775	+	0.473535i	$0.842978\pi$
$164$	−3.65078	−	6.32333i	−0.285078	−	0.493769i
$165$	−0.368292	−	0.312953i	−0.0286715	−	0.0243633i
$166$	−24.3092	−	14.0349i	−1.88676	−	1.08932i
$167$	−4.90398	−	8.49395i	−0.379482	−	0.657282i	0.611505	−	0.791240i	$-0.290564\pi$
$167$	−4.90398	−	8.49395i	−0.379482	−	0.657282i	−0.990987	+	0.133959i	$0.957231\pi$
$168$	5.71269	−	0.280244i	0.440744	−	0.0216213i
$169$	−3.25541	+	5.63854i	−0.250416	+	0.433734i
$170$	−3.28416	+	1.89611i	−0.251883	+	0.145425i
$171$	−14.8657	−	18.1699i	−1.13681	−	1.38949i
$172$	1.73735	−	3.00918i	0.132472	−	0.229448i
$173$	−2.97350			−0.226071			−0.113036	−	0.993591i	$-0.536057\pi$
$173$	−2.97350			−0.226071			−0.113036	+	0.993591i	$0.536057\pi$
$174$	−8.42417	−	23.6003i	−0.638635	−	1.78914i
$175$	2.53235	+	0.766281i	0.191428	+	0.0579254i
$176$	−1.18436	+	0.683789i	−0.0892743	+	0.0515425i
$177$	2.42011	−	2.84806i	0.181907	−	0.214073i
$178$	−8.43774	+	4.87153i	−0.632436	+	0.365137i
$179$	9.60988	+	5.54827i	0.718276	+	0.414697i	0.814118	−	0.580700i	$-0.197221\pi$
$179$	9.60988	+	5.54827i	0.718276	+	0.414697i	−0.0958418	+	0.995397i	$0.530554\pi$
$180$	3.68846	+	1.39462i	0.274921	+	0.103949i
$181$			17.3072i			1.28644i	0.765683	+	0.643218i	$0.222401\pi$
$181$			17.3072i			1.28644i	−0.765683	+	0.643218i	$0.777599\pi$
$182$	−11.7442	−	3.55376i	−0.870539	−	0.263422i
$183$	4.49377	+	3.81854i	0.332189	+	0.282275i
$184$	1.12129	−	1.94213i	0.0826625	−	0.143176i
$185$	−1.03345			−0.0759810
$186$	16.9072	−	19.8969i	1.23970	−	1.45891i
$187$		−	0.581225i		−	0.0425034i
$188$	−11.7951			−0.860244
$189$	13.4425	−	2.88100i	0.977795	−	0.209562i
$190$	−14.2466			−1.03356
$191$			10.8578i			0.785642i	0.919615	+	0.392821i	$0.128501\pi$
$191$			10.8578i			0.785642i	−0.919615	+	0.392821i	$0.871499\pi$
$192$	2.12839	−	2.50475i	0.153603	−	0.180765i
$193$	−6.28339			−0.452288			−0.226144	−	0.974094i	$-0.572612\pi$
$193$	−6.28339			−0.452288			−0.226144	+	0.974094i	$0.572612\pi$
$194$	8.02813	−	13.9051i	0.576386	−	0.998330i
$195$	3.36226	+	2.85705i	0.240776	+	0.204598i
$196$	−0.589157	+	9.18217i	−0.0420826	+	0.655869i
$197$		−	20.0865i		−	1.43110i	−0.698561	−	0.715551i	$-0.746176\pi$
$197$		−	20.0865i		−	1.43110i	0.698561	−	0.715551i	$-0.253824\pi$
$198$	−1.17952	+	0.965023i	−0.0838251	+	0.0685812i
$199$	19.3323	+	11.1615i	1.37043	+	0.791220i	0.990982	−	0.133991i	$-0.0427795\pi$
$199$	19.3323	+	11.1615i	1.37043	+	0.791220i	0.379451	+	0.925212i	$0.376113\pi$
$200$	−1.08090	+	0.624055i	−0.0764308	+	0.0441274i
$201$	−13.4238	+	15.7975i	−0.946840	+	1.11427i
$202$	−28.8057	+	16.6310i	−2.02676	+	1.17015i
$203$	−20.4728	+	4.78843i	−1.43691	+	0.336082i
$204$	1.59425	+	4.46629i	0.111620	+	0.312703i
$205$	5.55490			0.387971
$206$	12.0007	−	20.7858i	0.836129	−	1.44822i
$207$	1.90639	−	5.04196i	0.132503	−	0.350441i
$208$	10.8124	−	6.24253i	0.749704	−	0.432842i
$209$	1.09178	−	1.89101i	0.0755197	−	0.130804i
$210$	3.81240	−	7.42083i	0.263081	−	0.512086i
$211$	−0.255337	−	0.442257i	−0.0175781	−	0.0304462i	0.857103	−	0.515146i	$-0.172262\pi$
$211$	−0.255337	−	0.442257i	−0.0175781	−	0.0304462i	−0.874681	+	0.484700i	$0.838929\pi$
$212$	8.11206	+	4.68350i	0.557139	+	0.321664i
$213$	6.16654	+	5.23996i	0.422525	+	0.359036i
$214$	6.39031	+	11.0683i	0.436832	+	0.756616i
$215$	1.32175	+	2.28933i	0.0901423	+	0.156131i
$216$	−3.34678	+	5.55510i	−0.227719	+	0.377976i
$217$	−14.9868	−	15.9792i	−1.01737	−	1.08474i
$218$	16.1143	+	9.30362i	1.09140	+	0.630121i
$219$	−1.95116	+	0.696470i	−0.131847	+	0.0470631i
$220$			0.366771i			0.0247277i
$221$			5.30620i			0.356933i
$222$	−0.585807	+	3.20570i	−0.0393168	+	0.215153i
$223$	15.5316	+	8.96717i	1.04007	+	0.600486i	0.919854	−	0.392261i	$-0.128307\pi$
$223$	15.5316	+	8.96717i	1.04007	+	0.600486i	0.120219	+	0.992747i	$0.461640\pi$
$224$	−11.6317	−	12.4020i	−0.777178	−	0.828642i
$225$	−2.32191	+	1.89966i	−0.154794	+	0.126644i
$226$	10.4824	+	18.1560i	0.697276	+	1.20772i
$227$	5.53173	+	9.58123i	0.367154	+	0.635929i	0.989119	−	0.147116i	$-0.0469990\pi$
$227$	5.53173	+	9.58123i	0.367154	+	0.635929i	−0.621966	+	0.783044i	$0.713666\pi$
$228$	−3.20262	+	17.5257i	−0.212099	+	1.16067i
$229$	−23.1355	−	13.3573i	−1.52884	−	0.882676i	−0.999411	−	0.0343220i	$-0.989073\pi$
$229$	−23.1355	−	13.3573i	−1.52884	−	0.882676i	−0.529429	−	0.848354i	$-0.677594\pi$
$230$	−1.63557	−	2.83289i	−0.107846	−	0.186795i
$231$	0.692836	+	1.07472i	0.0455853	+	0.0707115i
$232$	4.95926	−	8.58970i	0.325592	−	0.563941i
$233$	−0.00408712	+	0.00235970i	−0.000267756	+	0.000154589i	−0.500134	−	0.865948i	$-0.666716\pi$
$233$	−0.00408712	+	0.00235970i	−0.000267756	+	0.000154589i	0.499866	+	0.866103i	$0.333383\pi$
$234$	10.7683	−	8.81001i	0.703943	−	0.575928i
$235$	4.48674	−	7.77126i	0.292683	−	0.506941i
$236$	−2.83630			−0.184627
$237$	12.6483	−	14.8849i	0.821594	−	0.966876i
$238$	9.76960	−	2.28503i	0.633269	−	0.148117i
$239$	13.1415	−	7.58726i	0.850054	−	0.490779i	−0.0106152	−	0.999944i	$-0.503379\pi$
$239$	13.1415	−	7.58726i	0.850054	−	0.490779i	0.860669	+	0.509165i	$0.170046\pi$
$240$	2.85380	+	7.99494i	0.184212	+	0.516071i
$241$	−8.38622	+	4.84179i	−0.540204	+	0.311887i	−0.745162	−	0.666884i	$-0.767628\pi$
$241$	−8.38622	+	4.84179i	−0.540204	+	0.311887i	0.204958	+	0.978771i	$0.434294\pi$
$242$	17.2204	+	9.94220i	1.10697	+	0.639109i
$243$	−5.78387	+	14.4757i	−0.371036	+	0.928619i
$244$		−	4.47522i		−	0.286496i
$245$	−5.82563	−	3.88099i	−0.372186	−	0.247947i
$246$	3.14876	−	17.2309i	0.200758	−	1.09860i
$247$	−9.96718	+	17.2637i	−0.634197	+	1.09846i
$248$	10.3347			0.656252
$249$	−8.97766	−	25.1509i	−0.568936	−	1.59388i
$250$			1.82056i			0.115142i
$251$	28.0986			1.77357			0.886784	−	0.462183i	$-0.152934\pi$
$251$	28.0986			1.77357			0.886784	+	0.462183i	$0.152934\pi$
$252$	−8.27180	−	6.35806i	−0.521075	−	0.400520i
$253$	0.501361			0.0315203
$254$			26.5535i			1.66612i
$255$	−3.54908	−	0.648556i	−0.222252	−	0.0406141i
$256$	20.9055			1.30659
$257$	4.06907	−	7.04783i	0.253822	−	0.439632i	−0.710753	−	0.703441i	$-0.751646\pi$
$257$	4.06907	−	7.04783i	0.253822	−	0.439632i	0.964575	+	0.263810i	$0.0849791\pi$
$258$	7.85058	−	2.80227i	0.488755	−	0.174462i
$259$	2.61707	+	0.791916i	0.162617	+	0.0492072i
$260$		−	3.34838i		−	0.207657i
$261$	8.43161	−	22.2997i	0.521904	−	1.38032i
$262$	5.22050	+	3.01406i	0.322524	+	0.186209i
$263$	−0.444017	+	0.256353i	−0.0273792	+	0.0158074i	−0.513627	−	0.858013i	$-0.671699\pi$
$263$	−0.444017	+	0.256353i	−0.0273792	+	0.0158074i	0.486248	+	0.873821i	$0.338365\pi$
$264$	−0.593385	−	0.108435i	−0.0365203	−	0.00667368i
$265$	−6.17152	+	3.56313i	−0.379113	+	0.218881i
$266$	36.0775	+	10.9169i	2.21205	+	0.669360i
$267$	−9.11840	−	1.66629i	−0.558037	−	0.101975i
$268$	15.7323			0.961001
$269$	0.187109	−	0.324082i	0.0114082	−	0.0197596i	−0.860265	−	0.509847i	$-0.829702\pi$
$269$	0.187109	−	0.324082i	0.0114082	−	0.0197596i	0.871673	+	0.490088i	$0.163035\pi$
$270$	4.57647	+	8.27923i	0.278515	+	0.503858i
$271$	−5.62493	+	3.24755i	−0.341690	+	0.197275i	−0.661019	−	0.750369i	$-0.729876\pi$
$271$	−5.62493	+	3.24755i	−0.341690	+	0.197275i	0.319329	+	0.947644i	$0.396542\pi$
$272$	−5.10452	+	8.84128i	−0.309507	+	0.536082i
$273$	−6.32513	−	9.81149i	−0.382814	−	0.593819i
$274$	8.72513	+	15.1124i	0.527104	+	0.912971i
$275$	−0.241650	−	0.139517i	−0.0145720	−	0.00841317i
$276$	−3.85259	+	1.37519i	−0.231899	+	0.0827765i
$277$	1.82390	+	3.15909i	0.109588	+	0.189811i	0.915603	−	0.402083i	$-0.131714\pi$
$277$	1.82390	+	3.15909i	0.109588	+	0.189811i	−0.806016	+	0.591894i	$0.798380\pi$
$278$	−1.61389	−	2.79534i	−0.0967949	−	0.167654i
$279$	24.5151	−	4.00931i	1.46768	−	0.240031i
$280$	3.21541	−	0.752059i	0.192157	−	0.0449441i
$281$	−2.85480	−	1.64822i	−0.170303	−	0.0983244i	0.412426	−	0.910991i	$-0.364682\pi$
$281$	−2.85480	−	1.64822i	−0.170303	−	0.0983244i	−0.582729	+	0.812667i	$0.698015\pi$
$282$	−21.5627	−	18.3227i	−1.28404	−	1.09110i
$283$		−	13.9433i		−	0.828842i	−0.910085	−	0.414421i	$-0.863984\pi$
$283$		−	13.9433i		−	0.828842i	0.910085	−	0.414421i	$-0.136016\pi$
$284$		−	6.14108i		−	0.364406i
$285$	−10.3287	−	8.77669i	−0.611817	−	0.519886i
$286$	1.12069	+	0.647032i	0.0662679	+	0.0382598i
$287$	−14.0670	−	4.25661i	−0.830346	−	0.251260i
$288$	19.0270	−	3.11176i	1.12117	−	0.183362i
$289$	6.33056	+	10.9649i	0.372386	+	0.644992i
$290$	−7.23384	−	12.5294i	−0.424786	−	0.735751i
$291$	14.3866	−	5.13532i	0.843358	−	0.301038i
$292$	1.36158	+	0.786110i	0.0796806	+	0.0460036i
$293$	−14.4552	−	25.0371i	−0.844482	−	1.46269i	−0.886070	−	0.463551i	$-0.846575\pi$
$293$	−14.4552	−	25.0371i	−0.844482	−	1.46269i	0.0415885	−	0.999135i	$-0.486758\pi$
$294$	−15.3408	+	15.8708i	−0.894693	+	0.925604i
$295$	1.07890	−	1.86871i	0.0628161	−	0.108801i
$296$	−1.11705	+	0.644932i	−0.0649275	+	0.0374859i
$297$	−1.44965	−	0.0270172i	−0.0841171	−	0.00156770i
$298$	−10.3132	+	17.8630i	−0.597430	+	1.03478i
$299$	−4.57709			−0.264700
$300$	2.23958	+	0.409259i	0.129302	+	0.0236286i
$301$	−1.59286	−	6.81022i	−0.0918107	−	0.392535i
$302$	−28.4919	+	16.4498i	−1.63952	+	0.946579i
$303$	−31.1294	−	5.68856i	−1.78834	−	0.326799i
$304$	−33.2150	+	19.1767i	−1.90501	+	1.09986i
$305$	2.94853	+	1.70233i	0.168832	+	0.0974753i
$306$	−4.02355	+	10.6414i	−0.230011	+	0.608328i
$307$		−	9.62077i		−	0.549086i	−0.961575	−	0.274543i	$-0.911473\pi$
$307$		−	9.62077i		−	0.549086i	0.961575	−	0.274543i	$-0.0885266\pi$
$308$	0.281050	−	0.928794i	0.0160143	−	0.0529230i
$309$	21.5056	−	7.67644i	1.22341	−	0.436697i
$310$	7.53735	−	13.0551i	0.428092	−	0.741478i
$311$	−3.05894			−0.173457			−0.0867284	−	0.996232i	$-0.527641\pi$
$311$	−3.05894			−0.173457			−0.0867284	+	0.996232i	$0.527641\pi$
$312$	5.41721	+	0.989934i	0.306689	+	0.0560440i
$313$		−	3.43805i		−	0.194330i	−0.995268	−	0.0971650i	$-0.969023\pi$
$313$		−	3.43805i		−	0.194330i	0.995268	−	0.0971650i	$-0.0309774\pi$
$314$	37.4131			2.11134
$315$	7.33558	−	3.03138i	0.413313	−	0.170799i
$316$	−14.8234			−0.833882
$317$		−	5.14140i		−	0.288770i	−0.989522	−	0.144385i	$-0.953880\pi$
$317$		−	5.14140i		−	0.288770i	0.989522	−	0.144385i	$-0.0461204\pi$
$318$	7.55430	+	21.1634i	0.423624	+	1.18678i
$319$	2.21743			0.124152
$320$	0.948852	−	1.64346i	0.0530424	−	0.0918722i
$321$	−2.18578	+	11.9612i	−0.121998	+	0.667609i
$322$	1.97105	+	8.42719i	0.109842	+	0.469629i
$323$		−	16.3003i		−	0.906974i
$324$	11.2136	−	3.76864i	0.622977	−	0.209369i
$325$	2.20610	+	1.27369i	0.122372	+	0.0706518i
$326$	−1.21961	+	0.704145i	−0.0675482	+	0.0389990i
$327$	5.95121	+	16.6723i	0.329103	+	0.921981i
$328$	6.00426	−	3.46656i	0.331530	−	0.191409i
$329$	−17.3170	+	16.2415i	−0.954716	+	0.895422i
$330$	−0.569749	+	0.670498i	−0.0313637	+	0.0369097i
$331$	11.5000			0.632096			0.316048	−	0.948743i	$-0.397644\pi$
$331$	11.5000			0.632096			0.316048	+	0.948743i	$0.397644\pi$
$332$	−10.1332	+	17.5511i	−0.556129	+	0.963244i
$333$	−2.39959	+	1.96321i	−0.131497	+	0.107583i
$334$	−15.4637	+	8.92799i	−0.846138	+	0.488518i
$335$	−5.98441	+	10.3653i	−0.326964	+	0.566317i
$336$	−1.10047	−	22.4328i	−0.0600358	−	1.22381i
$337$	8.53664	+	14.7859i	0.465020	+	0.805439i	0.999202	−	0.0399304i	$-0.0127136\pi$
$337$	8.53664	+	14.7859i	0.465020	+	0.805439i	−0.534182	+	0.845370i	$0.679380\pi$
$338$	10.2653	+	5.92667i	0.558358	+	0.322368i
$339$	−3.58544	+	19.6206i	−0.194735	+	1.06564i
$340$	1.36898	+	2.37115i	0.0742435	+	0.128594i
$341$	1.15523	+	2.00092i	0.0625594	+	0.108356i
$342$	−33.0794	+	27.0638i	−1.78873	+	1.46344i
$343$	11.7786	+	14.2921i	0.635986	+	0.771701i
$344$	2.85734	+	1.64968i	0.154057	+	0.0889450i
$345$	0.559439	−	3.06141i	0.0301192	−	0.164821i
$346$			5.41344i			0.291028i
$347$			4.41241i			0.236871i	0.992962	+	0.118435i	$0.0377878\pi$
$347$			4.41241i			0.236871i	−0.992962	+	0.118435i	$0.962212\pi$
$348$	−17.0393	+	6.08221i	−0.913404	+	0.326041i
$349$	−15.3333	−	8.85267i	−0.820771	−	0.473873i	0.0299110	−	0.999553i	$-0.490478\pi$
$349$	−15.3333	−	8.85267i	−0.820771	−	0.473873i	−0.850682	+	0.525680i	$0.823811\pi$
$350$	1.39506	−	4.61030i	0.0745691	−	0.246431i
$351$	13.2343	+	0.246649i	0.706395	+	0.0131652i
$352$	0.896614	+	1.55298i	0.0477897	+	0.0827742i
$353$	−1.55710	−	2.69697i	−0.0828759	−	0.143545i	0.821608	−	0.570053i	$-0.193077\pi$
$353$	−1.55710	−	2.69697i	−0.0828759	−	0.143545i	−0.904484	+	0.426507i	$0.859744\pi$
$354$	−5.18506	−	4.40595i	−0.275583	−	0.234174i
$355$	4.04609	+	2.33601i	0.214744	+	0.123983i
$356$	3.51723	+	6.09201i	0.186413	+	0.322876i
$357$	8.49056	+	4.36197i	0.449368	+	0.230860i
$358$	10.1009	−	17.4954i	0.533852	−	0.924658i
$359$	9.45069	−	5.45636i	0.498788	−	0.287975i	−0.229425	−	0.973326i	$-0.573685\pi$
$359$	9.45069	−	5.45636i	0.498788	−	0.287975i	0.728213	+	0.685351i	$0.240351\pi$
$360$	−1.32425	+	3.50234i	−0.0697940	+	0.184589i
$361$	21.1186	−	36.5785i	1.11150	−	1.92518i
$362$	31.5089			1.65607
$363$	6.35969	+	17.8167i	0.333797	+	0.935133i
$364$	−2.56580	+	8.47927i	−0.134484	+	0.444434i
$365$	−1.03587	+	0.598059i	−0.0542199	+	0.0313039i
$366$	6.95188	−	8.18118i	0.363381	−	0.427637i
$367$	−4.05032	+	2.33845i	−0.211425	+	0.122066i	−0.601973	−	0.798516i	$-0.705619\pi$
$367$	−4.05032	+	2.33845i	−0.211425	+	0.122066i	0.390548	+	0.920582i	$0.372285\pi$
$368$	−7.62643	−	4.40312i	−0.397555	−	0.229529i
$369$	12.8980	−	10.5524i	0.671442	−	0.549338i
$370$			1.88146i			0.0978126i
$371$	18.3588	−	4.29398i	0.953142	−	0.222932i
$372$	−14.3655	−	12.2069i	−0.744815	−	0.632899i
$373$	15.7359	−	27.2554i	0.814775	−	1.41123i	−0.0947137	−	0.995505i	$-0.530194\pi$
$373$	15.7359	−	27.2554i	0.814775	−	1.41123i	0.909489	−	0.415728i	$-0.136473\pi$
$374$	−1.05815			−0.0547159
$375$	−1.12156	+	1.31989i	−0.0579172	+	0.0681587i
$376$		−	11.1999i		−	0.577591i
$377$	−20.2437			−1.04260
$378$	−5.24503	−	24.4728i	−0.269775	−	1.25875i
$379$	−7.31121			−0.375551			−0.187776	−	0.982212i	$-0.560128\pi$
$379$	−7.31121			−0.375551			−0.187776	+	0.982212i	$0.560128\pi$
$380$			10.2860i			0.527661i
$381$	−16.3584	+	19.2510i	−0.838066	+	0.986261i
$382$	19.7672			1.01138
$383$	−17.1511	+	29.7066i	−0.876380	+	1.51794i	−0.0210951	+	0.999777i	$0.506715\pi$
$383$	−17.1511	+	29.7066i	−0.876380	+	1.51794i	−0.855285	+	0.518158i	$0.826618\pi$
$384$	12.4047	+	10.5407i	0.633022	+	0.537905i
$385$	0.505034	+	0.538477i	0.0257389	+	0.0274433i
$386$			11.4393i			0.582244i
$387$	7.41794	+	2.80475i	0.377075	+	0.142573i
$388$	−10.0394	−	5.79628i	−0.509676	−	0.294261i
$389$	−24.4881	+	14.1382i	−1.24160	+	0.716837i	−0.969419	−	0.245410i	$-0.921078\pi$
$389$	−24.4881	+	14.1382i	−1.24160	+	0.716837i	−0.272179	+	0.962247i	$0.587744\pi$
$390$	5.20143	−	6.12119i	0.263384	−	0.309959i
$391$	3.24126	−	1.87134i	0.163917	−	0.0946378i
$392$	−8.71884	−	0.559428i	−0.440368	−	0.0282554i
$393$	1.92799	+	5.40126i	0.0972542	+	0.272458i
$394$	−36.5686			−1.84230
$395$	5.63869	−	9.76650i	0.283713	−	0.491406i
$396$	0.696742	+	0.851611i	0.0350126	+	0.0427950i
$397$	−3.85562	+	2.22604i	−0.193508	+	0.111722i	−0.593624	−	0.804743i	$-0.702303\pi$
$397$	−3.85562	+	2.22604i	−0.193508	+	0.111722i	0.400116	+	0.916465i	$0.368970\pi$
$398$	20.3202	−	35.1957i	1.01856	−	1.76420i
$399$	19.4304	+	30.1403i	0.972738	+	1.50890i
$400$	2.45057	+	4.24450i	0.122528	+	0.212225i
$401$	−12.6924	−	7.32795i	−0.633827	−	0.365940i	0.148406	−	0.988927i	$-0.452586\pi$
$401$	−12.6924	−	7.32795i	−0.633827	−	0.365940i	−0.782233	+	0.622986i	$0.785919\pi$
$402$	28.7603	+	24.4388i	1.43443	+	1.21890i
$403$	−10.5465	−	18.2671i	−0.525359	−	0.909948i
$404$	12.0075	+	20.7976i	0.597396	+	1.03472i
$405$	−1.78255	+	8.82171i	−0.0885756	+	0.438354i
$406$	8.71762	+	37.2720i	0.432648	+	1.84978i
$407$	−0.249734	−	0.144184i	−0.0123788	−	0.00714693i
$408$	−4.24092	+	1.51380i	−0.209957	+	0.0749444i
$409$			13.2710i			0.656211i	0.944641	+	0.328105i	$0.106410\pi$
$409$			13.2710i			0.656211i	−0.944641	+	0.328105i	$0.893590\pi$
$410$		−	10.1130i		−	0.499446i
$411$	−2.98439	+	16.3315i	−0.147209	+	0.805571i
$412$	−15.0073	−	8.66445i	−0.739355	−	0.426867i
$413$	−4.16412	+	3.90550i	−0.204903	+	0.192177i
$414$	−9.17919	−	3.47069i	−0.451133	−	0.170575i
$415$	−7.70913	−	13.3526i	−0.378426	−	0.655453i
$416$	−8.18549	−	14.1777i	−0.401326	−	0.695118i
$417$	0.552025	−	3.02084i	0.0270328	−	0.147931i
$418$	−3.44270	−	1.98764i	−0.168388	−	0.0972188i
$419$	−18.8571	−	32.6614i	−0.921227	−	1.59561i	−0.797519	−	0.603294i	$-0.793855\pi$
$419$	−18.8571	−	32.6614i	−0.921227	−	1.59561i	−0.123708	−	0.992319i	$-0.539479\pi$
$420$	−5.35781	−	2.75254i	−0.261434	−	0.134310i
$421$	17.0455	−	29.5237i	0.830749	−	1.43890i	−0.0666970	−	0.997773i	$-0.521246\pi$
$421$	17.0455	−	29.5237i	0.830749	−	1.43890i	0.897446	−	0.441125i	$-0.145421\pi$
$422$	−0.805155	+	0.464856i	−0.0391943	+	0.0226288i
$423$	−4.34497	−	26.5675i	−0.211260	−	1.29176i
$424$	−4.44718	+	7.70273i	−0.215974	+	0.374078i
$425$	−2.08300			−0.101040
$426$	9.53966	−	11.2266i	0.462198	−	0.543929i
$427$	−6.16225	−	6.57031i	−0.298212	−	0.317960i
$428$	7.99129	−	4.61377i	0.386274	−	0.223015i
$429$	0.413884	+	1.15950i	0.0199825	+	0.0559810i
$430$	4.16786	−	2.40632i	0.200992	−	0.116043i
$431$	23.9166	+	13.8082i	1.15202	+	0.665119i	0.949379	−	0.314134i	$-0.101714\pi$
$431$	23.9166	+	13.8082i	1.15202	+	0.665119i	0.202642	+	0.979253i	$0.435047\pi$
$432$	21.8140	+	13.1423i	1.04953	+	0.632308i
$433$		−	7.35963i		−	0.353681i	−0.984239	−	0.176841i	$-0.943412\pi$
$433$		−	7.35963i		−	0.353681i	0.984239	−	0.176841i	$-0.0565877\pi$
$434$	−29.0911	+	27.2843i	−1.39642	+	1.30969i
$435$	2.47430	−	13.5401i	0.118634	−	0.649198i
$436$	6.71717	−	11.6345i	0.321694	−	0.557191i
$437$	14.0605			0.672607
$438$	1.26796	+	3.55220i	0.0605857	+	0.169731i
$439$			4.51571i			0.215523i	0.994177	+	0.107762i	$0.0343683\pi$
$439$			4.51571i			0.215523i	−0.994177	+	0.107762i	$0.965632\pi$
$440$	−0.348264			−0.0166028
$441$	−20.8992	+	2.05542i	−0.995198	+	0.0978774i
$442$	9.66024			0.459491
$443$			31.6469i			1.50359i	0.659397	+	0.751795i	$0.270812\pi$
$443$			31.6469i			1.50359i	−0.659397	+	0.751795i	$0.729188\pi$
$444$	2.31450	+	0.422950i	0.109842	+	0.0200723i
$445$	−5.35169			−0.253694
$446$	16.3253	−	28.2762i	0.773024	−	1.33892i
$447$	−18.4816	+	6.59703i	−0.874149	+	0.312029i
$448$	−3.66218	+	3.43473i	−0.173022	+	0.162276i
$449$		−	33.1966i		−	1.56664i	−0.621617	−	0.783322i	$-0.713524\pi$
$449$		−	33.1966i		−	1.56664i	0.621617	−	0.783322i	$-0.286476\pi$
$450$	3.45845	+	4.22718i	0.163033	+	0.199271i
$451$	1.34234	+	0.775000i	0.0632083	+	0.0364933i
$452$	13.1085	−	7.56822i	0.616574	−	0.355979i
$453$	−30.7902	−	5.62657i	−1.44665	−	0.264360i
$454$	17.4432	−	10.0708i	0.818650	−	0.472648i
$455$	−4.61062	−	4.91593i	−0.216149	−	0.230463i
$456$	−16.6413	−	3.04102i	−0.779302	−	0.142409i
$457$	8.06568			0.377297			0.188648	−	0.982045i	$-0.439589\pi$
$457$	8.06568			0.377297			0.188648	+	0.982045i	$0.439589\pi$
$458$	−24.3178	+	42.1196i	−1.13630	+	1.96812i
$459$	−9.47270	+	5.23618i	−0.442148	+	0.244404i
$460$	−2.04533	+	1.18087i	−0.0953642	+	0.0550586i
$461$	−7.24840	+	12.5546i	−0.337592	+	0.584726i	−0.983979	−	0.178284i	$-0.942946\pi$
$461$	−7.24840	+	12.5546i	−0.337592	+	0.584726i	0.646388	+	0.763009i	$0.276279\pi$
$462$	1.95660	−	1.26135i	0.0910291	−	0.0586833i
$463$	−20.4326	−	35.3903i	−0.949583	−	1.64473i	−0.746304	−	0.665606i	$-0.768173\pi$
$463$	−20.4326	−	35.3903i	−0.949583	−	1.64473i	−0.203280	−	0.979121i	$-0.565160\pi$
$464$	−33.7304	−	19.4742i	−1.56589	−	0.904069i
$465$	13.5071	−	4.82138i	0.626377	−	0.223586i
$466$	0.00429597	+	0.00744084i	0.000199007	+	0.000344690i
$467$	6.08030	+	10.5314i	0.281363	+	0.487334i	0.971721	−	0.236134i	$-0.0758803\pi$
$467$	6.08030	+	10.5314i	0.281363	+	0.487334i	−0.690358	+	0.723468i	$0.742547\pi$
$468$	−6.36079	−	7.77463i	−0.294028	−	0.359383i
$469$	23.0974	−	21.6629i	1.06654	−	1.00030i
$470$	−14.1480	−	8.16838i	−0.652601	−	0.376779i
$471$	27.1241	+	23.0484i	1.24981	+	1.06202i
$472$		−	2.69318i		−	0.123964i
$473$			0.737622i			0.0339159i
$474$	−27.0988	−	23.0269i	−1.24469	−	1.05766i
$475$	−6.77701	−	3.91271i	−0.310951	−	0.179527i
$476$	−1.64978	−	7.05361i	−0.0756177	−	0.323302i
$477$	−7.56097	+	19.9971i	−0.346193	+	0.915603i
$478$	−13.8130	−	23.9249i	−0.631794	−	1.09430i
$479$	−11.8744	−	20.5671i	−0.542556	−	0.939735i	−0.998756	−	0.0498575i	$-0.984123\pi$
$479$	−11.8744	−	20.5671i	−0.542556	−	0.939735i	0.456200	−	0.889877i	$-0.349210\pi$
$480$	10.4833	−	3.74203i	0.478496	−	0.170800i
$481$	2.27990	+	1.31630i	0.103955	+	0.0600182i
$482$	8.81476	+	15.2676i	0.401501	+	0.695420i
$483$	−3.76260	+	7.32390i	−0.171204	+	0.333249i
$484$	7.17823	−	12.4331i	0.326283	−	0.565139i
$485$	7.63783	−	4.40971i	0.346816	−	0.200234i
$486$	26.3539	+	10.5299i	1.19544	+	0.477645i
$487$	−14.7059	+	25.4713i	−0.666386	+	1.15422i	0.312521	+	0.949911i	$0.398827\pi$
$487$	−14.7059	+	25.4713i	−0.666386	+	1.15422i	−0.978907	+	0.204304i	$0.934507\pi$
$488$	4.24940			0.192361
$489$	−1.31800	−	0.240850i	−0.0596020	−	0.0108916i
$490$	−7.06557	+	10.6059i	−0.319190	+	0.479126i
$491$	−24.5640	+	14.1821i	−1.10856	+	0.640027i	−0.938456	−	0.345399i	$-0.887744\pi$
$491$	−24.5640	+	14.1821i	−1.10856	+	0.640027i	−0.170103	+	0.985426i	$0.554410\pi$
$492$	−12.4406	−	2.27339i	−0.560868	−	0.102492i
$493$	14.3355	−	8.27662i	0.645639	−	0.372760i
$494$	31.4295	+	18.1458i	1.41408	+	0.816420i
$495$	−0.826124	+	0.135108i	−0.0371315	+	0.00607267i
$496$		−	40.5826i		−	1.82221i
$497$	−8.45610	−	9.01605i	−0.379308	−	0.404425i
$498$	−45.7888	+	16.3444i	−2.05184	+	0.732408i
$499$	16.6847	−	28.8987i	0.746909	−	1.29368i	−0.202388	−	0.979305i	$-0.564870\pi$
$499$	16.6847	−	28.8987i	0.746909	−	1.29368i	0.949297	−	0.314379i	$-0.101796\pi$
$500$	1.31444			0.0587834
$501$	−16.7112	−	3.05378i	−0.746600	−	0.136433i
$502$		−	51.1552i		−	2.28317i
$503$	−22.5856			−1.00704			−0.503522	−	0.863983i	$-0.667963\pi$
$503$	−22.5856			−1.00704			−0.503522	+	0.863983i	$0.667963\pi$
$504$	6.03724	−	7.85441i	0.268920	−	0.349863i
$505$	−18.2702			−0.813014
$506$		−	0.912757i		−	0.0405770i
$507$	3.79109	+	10.6207i	0.168368	+	0.471684i
$508$	19.1715			0.850599
$509$	−4.68749	+	8.11898i	−0.207769	+	0.359867i	−0.951012	−	0.309155i	$-0.899954\pi$
$509$	−4.68749	+	8.11898i	−0.207769	+	0.359867i	0.743242	+	0.669023i	$0.233287\pi$
$510$	−1.18073	+	6.46132i	−0.0522838	+	0.286112i
$511$	3.08147	−	0.720731i	0.136316	−	0.0318833i
$512$		−	19.2632i		−	0.851321i
$513$	−40.6550	−	0.757691i	−1.79496	−	0.0334529i
$514$	−12.8310	−	7.40798i	−0.565951	−	0.326752i
$515$	11.4173	−	6.59177i	0.503105	−	0.290468i
$516$	−2.02323	−	5.66808i	−0.0890677	−	0.249523i
$517$	2.16844	−	1.25195i	0.0953679	−	0.0550607i
$518$	1.44173	−	4.76453i	0.0633459	−	0.209341i
$519$	−3.33497	+	3.92469i	−0.146389	+	0.172275i
$520$	3.17942			0.139427
$521$	−5.18548	+	8.98151i	−0.227180	+	0.393487i	−0.956971	−	0.290183i	$-0.906284\pi$
$521$	−5.18548	+	8.98151i	−0.227180	+	0.393487i	0.729791	+	0.683670i	$0.239617\pi$
$522$	−40.5980	−	15.3503i	−1.77692	−	0.671862i
$523$	20.2717	−	11.7039i	0.886419	−	0.511774i	0.0136495	−	0.999907i	$-0.495655\pi$
$523$	20.2717	−	11.7039i	0.886419	−	0.511774i	0.872769	+	0.488133i	$0.162322\pi$
$524$	2.17614	−	3.76918i	0.0950649	−	0.164657i
$525$	3.85159	−	2.48299i	0.168097	−	0.108367i
$526$	0.466706	+	0.808358i	0.0203493	+	0.0352461i
$527$	14.9370	+	8.62387i	0.650665	+	0.375662i
$528$	−0.425805	+	2.33013i	−0.0185308	+	0.101406i
$529$	−9.88579	−	17.1227i	−0.429817	−	0.744465i
$530$	6.48688	+	11.2356i	0.281772	+	0.488044i
$531$	−1.04481	−	6.38854i	−0.0453410	−	0.277239i
$532$	7.88197	−	26.0478i	0.341727	−	1.12932i
$533$	−12.2547	−	7.07523i	−0.530808	−	0.306462i
$534$	−3.03357	+	16.6006i	−0.131276	+	0.718378i
$535$			7.02016i			0.303508i
$536$			14.9384i			0.645241i
$537$	18.1011	−	6.46123i	0.781122	−	0.278823i
$538$	−0.590011	−	0.340643i	−0.0254372	−	0.0146862i
$539$	−0.866300	−	1.75061i	−0.0373142	−	0.0754042i
$540$	5.97757	−	3.30419i	0.257234	−	0.142190i
$541$	−0.818259	−	1.41727i	−0.0351797	−	0.0609330i	0.847899	−	0.530157i	$-0.177867\pi$
$541$	−0.818259	−	1.41727i	−0.0351797	−	0.0609330i	−0.883079	+	0.469224i	$0.844534\pi$
$542$	5.91236	+	10.2405i	0.253958	+	0.439868i
$543$	22.8436	+	19.4111i	0.980312	+	0.833011i
$544$	11.5931	+	6.69327i	0.497049	+	0.286972i
$545$	5.11031	+	8.85131i	0.218902	+	0.379149i
$546$	−17.8624	+	11.5153i	−0.764440	+	0.492808i
$547$	−2.64181	+	4.57574i	−0.112956	+	0.195645i	−0.916961	−	0.398978i	$-0.869365\pi$
$547$	−2.64181	+	4.57574i	−0.112956	+	0.195645i	0.804005	+	0.594622i	$0.202698\pi$
$548$	10.9111	−	6.29950i	0.466097	−	0.269102i
$549$	10.0801	−	1.64855i	0.430207	−	0.0703582i
$550$	−0.253998	+	0.439938i	−0.0108305	+	0.0187590i
$551$	62.1873			2.64927
$552$	−1.30580	−	3.65819i	−0.0555784	−	0.155703i
$553$	−21.7631	+	20.4114i	−0.925459	+	0.867982i
$554$	5.75131	−	3.32052i	0.244350	−	0.141075i
$555$	−1.15908	+	1.36404i	−0.0492003	+	0.0579003i
$556$	−2.01823	+	1.16522i	−0.0855919	+	0.0494165i
$557$	33.7106	+	19.4628i	1.42837	+	0.824667i	0.996992	−	0.0775063i	$-0.0246958\pi$
$557$	33.7106	+	19.4628i	1.42837	+	0.824667i	0.431374	+	0.902173i	$0.358029\pi$
$558$	−7.29919	−	44.6311i	−0.308999	−	1.88939i
$559$		−	6.73399i		−	0.284818i
$560$	−2.95322	−	12.6264i	−0.124796	−	0.533563i
$561$	−0.767151	−	0.651880i	−0.0323892	−	0.0275224i
$562$	−3.00068	+	5.19733i	−0.126576	+	0.219236i
$563$	28.2073			1.18879			0.594397	−	0.804171i	$-0.297391\pi$
$563$	28.2073			1.18879			0.594397	+	0.804171i	$0.297391\pi$
$564$	−13.2289	+	15.5682i	−0.557037	+	0.655537i
$565$			11.5155i			0.484462i
$566$	−25.3846			−1.06699
$567$	11.2740	−	20.9737i	0.473462	−	0.880815i
$568$	5.83120			0.244672
$569$		−	34.7556i		−	1.45703i	−0.685031	−	0.728514i	$-0.740211\pi$
$569$		−	34.7556i		−	1.45703i	0.685031	−	0.728514i	$-0.259789\pi$
$570$	−15.9785	+	18.8039i	−0.669265	+	0.787611i
$571$	8.83401			0.369692			0.184846	−	0.982768i	$-0.440821\pi$
$571$	8.83401			0.369692			0.184846	+	0.982768i	$0.440821\pi$
$572$	0.467154	−	0.809134i	0.0195327	−	0.0338316i
$573$	14.3310	+	12.1777i	0.598688	+	0.508729i
$574$	−7.74941	+	25.6097i	−0.323454	+	1.06893i
$575$		−	1.79678i		−	0.0749308i
$576$	−0.918871	−	5.61847i	−0.0382863	−	0.234103i
$577$	−23.9018	−	13.7997i	−0.995047	−	0.574491i	−0.0882679	−	0.996097i	$-0.528133\pi$
$577$	−23.9018	−	13.7997i	−0.995047	−	0.574491i	−0.906779	+	0.421606i	$0.861466\pi$
$578$	19.9622	−	11.5252i	0.830317	−	0.479384i
$579$	−7.04720	+	8.29336i	−0.292872	+	0.344660i
$580$	−9.04616	+	5.22280i	−0.375621	+	0.216865i
$581$	9.29039	+	39.7209i	0.385430	+	1.64790i
$582$	−9.34916	−	26.1917i	−0.387535	−	1.08568i
$583$	−1.98846			−0.0823537
$584$	−0.746444	+	1.29288i	−0.0308881	+	0.0534997i
$585$	7.54196	−	1.23345i	0.311822	−	0.0509968i
$586$	−45.5816	+	26.3166i	−1.88296	+	1.08713i
$587$	−3.99098	+	6.91258i	−0.164725	+	0.285313i	−0.936558	−	0.350513i	$-0.886007\pi$
$587$	−3.99098	+	6.91258i	−0.164725	+	0.285313i	0.771832	+	0.635826i	$0.219340\pi$
$588$	11.4586	+	11.0760i	0.472547	+	0.456766i
$589$	32.3982	+	56.1154i	1.33495	+	2.31219i
$590$	−3.40210	−	1.96421i	−0.140062	−	0.0808651i
$591$	−26.5119	−	22.5282i	−1.09055	−	0.926686i
$592$	2.53254	+	4.38650i	0.104087	+	0.180284i
$593$	3.87546	+	6.71249i	0.159146	+	0.275649i	0.934561	−	0.355803i	$-0.115793\pi$
$593$	3.87546	+	6.71249i	0.159146	+	0.275649i	−0.775415	+	0.631452i	$0.782459\pi$
$594$	−0.0491864	+	2.63917i	−0.00201814	+	0.108286i
$595$	5.27488	+	1.59616i	0.216249	+	0.0654362i
$596$	12.8970	+	7.44611i	0.528283	+	0.305005i
$597$	36.4144	−	12.9982i	1.49034	−	0.531979i
$598$			8.33286i			0.340756i
$599$		−	24.5095i		−	1.00143i	−0.865612	−	0.500715i	$-0.833071\pi$
$599$		−	24.5095i		−	1.00143i	0.865612	−	0.500715i	$-0.166929\pi$
$600$	−0.388608	+	2.12658i	−0.0158649	+	0.0868171i
$601$	12.3323	+	7.12006i	0.503046	+	0.290433i	0.729970	−	0.683479i	$-0.239534\pi$
$601$	12.3323	+	7.12006i	0.503046	+	0.290433i	−0.226925	+	0.973912i	$0.572867\pi$
$602$	−12.3984	+	2.89989i	−0.505322	+	0.118191i
$603$	5.79533	+	35.4357i	0.236004	+	1.44305i
$604$	11.8767	+	20.5710i	0.483255	+	0.837022i
$605$	5.46107	+	9.45885i	0.222024	+	0.384557i
$606$	−10.3564	+	56.6730i	−0.420698	+	2.30218i
$607$	2.26688	+	1.30878i	0.0920098	+	0.0531219i	0.545299	−	0.838242i	$-0.316416\pi$
$607$	2.26688	+	1.30878i	0.0920098	+	0.0531219i	−0.453289	+	0.891364i	$0.649749\pi$
$608$	25.1453	+	43.5530i	1.01978	+	1.76631i
$609$	−16.6413	+	32.3923i	−0.674341	+	1.31260i
$610$	3.09920	−	5.36797i	0.125483	−	0.217343i
$611$	−19.7964	+	11.4295i	−0.800877	+	0.462387i
$612$	7.68304	+	2.90499i	0.310569	+	0.117427i
$613$	−9.63669	+	16.6912i	−0.389222	+	0.674152i	−0.992345	−	0.123496i	$-0.960589\pi$
$613$	−9.63669	+	16.6912i	−0.389222	+	0.674152i	0.603123	+	0.797648i	$0.293923\pi$
$614$	−17.5152			−0.706855
$615$	6.23015	−	7.33183i	0.251224	−	0.295648i
$616$	0.881928	+	0.266868i	0.0355339	+	0.0107524i
$617$	12.9304	−	7.46538i	0.520559	−	0.300545i	−0.216604	−	0.976260i	$-0.569498\pi$
$617$	12.9304	−	7.46538i	0.520559	−	0.300545i	0.737163	+	0.675714i	$0.236165\pi$
$618$	−13.9754	−	39.1521i	−0.562174	−	1.57493i
$619$	2.72213	−	1.57162i	0.109412	−	0.0631688i	−0.444296	−	0.895880i	$-0.646546\pi$
$619$	2.72213	−	1.57162i	0.109412	−	0.0631688i	0.553707	+	0.832711i	$0.313213\pi$
$620$	−9.42570	−	5.44193i	−0.378545	−	0.218553i
$621$	−4.51669	−	8.17108i	−0.181249	−	0.327894i
$622$			5.56899i			0.223296i
$623$	13.5524	+	4.10090i	0.542964	+	0.164299i
$624$	3.88731	−	21.2725i	0.155617	−	0.851582i
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	−6.25917			−0.250167
$627$	−1.27143	−	3.56191i	−0.0507759	−	0.142249i
$628$		−	27.0121i		−	1.07790i
$629$	−2.15268			−0.0858330
$630$	−5.51882	−	13.3549i	−0.219875	−	0.532070i
$631$	−4.71364			−0.187647			−0.0938235	−	0.995589i	$-0.529909\pi$
$631$	−4.71364			−0.187647			−0.0938235	+	0.995589i	$0.529909\pi$
$632$		−	14.0754i		−	0.559890i
$633$	−0.870105	−	0.159002i	−0.0345836	−	0.00631976i
$634$	−9.36023			−0.371742
$635$	−7.29269	+	12.6313i	−0.289401	+	0.501258i
$636$	15.2799	−	5.45417i	0.605886	−	0.216272i
$637$	7.90874	+	15.9819i	0.313355	+	0.633226i
$638$		−	4.03697i		−	0.159825i
$639$	13.8323	−	2.26220i	0.547198	−	0.0894913i
$640$	8.13914	+	4.69914i	0.321728	+	0.185750i
$641$	−40.1571	+	23.1847i	−1.58611	+	0.915741i	−0.592171	+	0.805812i	$0.701729\pi$
$641$	−40.1571	+	23.1847i	−1.58611	+	0.915741i	−0.993939	+	0.109929i	$0.964938\pi$
$642$	21.7761	+	3.97933i	0.859433	+	0.157052i
$643$	−15.9868	+	9.23001i	−0.630460	+	0.363996i	−0.780930	−	0.624618i	$-0.785255\pi$
$643$	−15.9868	+	9.23001i	−0.630460	+	0.363996i	0.150470	+	0.988615i	$0.451921\pi$
$644$	6.08439	−	1.42309i	0.239759	−	0.0560776i
$645$	4.50408	+	0.823070i	0.177348	+	0.0324083i
$646$	−29.6757			−1.16757
$647$	−9.35740	+	16.2075i	−0.367877	+	0.637182i	−0.989233	−	0.146346i	$-0.953249\pi$
$647$	−9.35740	+	16.2075i	−0.367877	+	0.637182i	0.621356	+	0.783528i	$0.286582\pi$
$648$	3.57848	+	10.6478i	0.140576	+	0.418283i
$649$	0.521433	−	0.301050i	0.0204680	−	0.0118172i
$650$	2.31883	−	4.01634i	0.0909521	−	0.157534i
$651$	−37.8993	+	1.85921i	−1.48539	+	0.0728680i
$652$	0.508390	+	0.880557i	0.0199101	+	0.0344853i
$653$	24.8069	+	14.3223i	0.970768	+	0.560473i	0.899470	−	0.436982i	$-0.143953\pi$
$653$	24.8069	+	14.3223i	0.970768	+	0.560473i	0.0712980	+	0.997455i	$0.477286\pi$
$654$	30.3529	−	10.8345i	1.18689	−	0.423664i
$655$	1.65557	+	2.86753i	0.0646883	+	0.112043i
$656$	−13.6126	−	23.5778i	−0.531484	−	0.920557i
$657$	−1.26908	+	3.35644i	−0.0495117	+	0.130947i
$658$	29.5686	+	31.5266i	1.15270	+	1.22903i
$659$	−29.6315	−	17.1078i	−1.15428	−	0.666424i	−0.204354	−	0.978897i	$-0.565509\pi$
$659$	−29.6315	−	17.1078i	−1.15428	−	0.666424i	−0.949927	+	0.312473i	$0.898843\pi$
$660$	0.484096	+	0.411356i	0.0188434	+	0.0160120i
$661$			26.7687i			1.04118i	0.853806	+	0.520591i	$0.174288\pi$
$661$			26.7687i			1.04118i	−0.853806	+	0.520591i	$0.825712\pi$
$662$		−	20.9364i		−	0.813716i
$663$	7.00358	+	5.95122i	0.271996	+	0.231126i
$664$	−16.6655	−	9.62184i	−0.646747	−	0.373400i
$665$	14.1636	+	15.1015i	0.549239	+	0.585609i
$666$	3.57415	+	4.36859i	0.138495	+	0.169279i
$667$	7.13935	+	12.3657i	0.276437	+	0.478802i
$668$	6.44597	+	11.1648i	0.249402	+	0.431977i
$669$	29.2553	−	10.4427i	1.13107	−	0.403739i
$670$	18.8707	+	10.8950i	0.729037	+	0.420910i
$671$	0.475008	+	0.822737i	0.0183375	+	0.0317614i
$672$	−29.4149	+	1.44299i	−1.13470	+	0.0556646i
$673$	−11.4116	+	19.7654i	−0.439884	+	0.761902i	−0.997680	−	0.0680765i	$-0.978314\pi$
$673$	−11.4116	+	19.7654i	−0.439884	+	0.761902i	0.557796	+	0.829978i	$0.311647\pi$
$674$	26.9186	−	15.5415i	1.03687	−	0.598635i
$675$	−0.0968244	+	5.19525i	−0.00372677	+	0.199965i
$676$	4.27903	−	7.41150i	0.164578	−	0.285058i
$677$	25.7772			0.990697			0.495349	−	0.868694i	$-0.335040\pi$
$677$	25.7772			0.990697			0.495349	+	0.868694i	$0.335040\pi$
$678$	35.7204	+	6.52751i	1.37184	+	0.250688i
$679$	−22.7208	+	5.31421i	−0.871943	+	0.203941i
$680$	−2.25150	+	1.29990i	−0.0863411	+	0.0498491i
$681$	18.8503	+	3.44468i	0.722345	+	0.132001i
$682$	3.64280	−	2.10317i	0.139490	−	0.0805345i
$683$	15.4429	+	8.91598i	0.590907	+	0.341161i	0.765456	−	0.643488i	$-0.222513\pi$
$683$	15.4429	+	8.91598i	0.590907	+	0.341161i	−0.174549	+	0.984649i	$0.555847\pi$
$684$	19.5400	+	23.8832i	0.747129	+	0.913197i
$685$			9.58511i			0.366228i
$686$	26.0196	−	21.4437i	0.993433	−	0.818723i
$687$	−43.5781	+	15.5553i	−1.66261	+	0.593470i
$688$	6.47805	−	11.2203i	0.246973	−	0.427770i
$689$	18.1533			0.691586
$690$	−5.57349	−	1.01849i	−0.212179	−	0.0387733i
$691$		−	34.4883i		−	1.31200i	−0.754762	−	0.655998i	$-0.772248\pi$
$691$		−	34.4883i		−	1.31200i	0.754762	−	0.655998i	$-0.227752\pi$
$692$	3.90848			0.148578
$693$	2.19557	+	0.290901i	0.0834028	+	0.0110504i
$694$	8.03305			0.304931
$695$		−	1.77296i		−	0.0672523i
$696$	−5.77531	−	16.1795i	−0.218913	−	0.613284i
$697$	11.5708			0.438276
$698$	−16.1168	+	27.9151i	−0.610030	+	1.05660i
$699$	−0.00146942	+	0.00804107i	−5.55784e−5	+	0.000304141i
$700$	−3.32862	−	1.00723i	−0.125810	−	0.0380696i
$701$		−	18.2242i		−	0.688319i	−0.938911	−	0.344159i	$-0.888164\pi$
$701$		−	18.2242i		−	0.688319i	0.938911	−	0.344159i	$-0.111836\pi$
$702$	0.449039	−	24.0938i	0.0169479	−	0.909363i
$703$	−7.00373	−	4.04360i	−0.264151	−	0.152507i
$704$	0.458580	−	0.264761i	0.0172834	−	0.00997856i
$705$	−5.22503	−	14.6379i	−0.196786	−	0.551297i
$706$	−4.90999	+	2.83479i	−0.184790	+	0.106689i
$707$	46.2666	+	14.0001i	1.74004	+	0.526528i
$708$	−3.18108	+	3.74359i	−0.119552	+	0.140693i
$709$	27.0519			1.01595			0.507977	−	0.861371i	$-0.330393\pi$
$709$	27.0519			1.01595			0.507977	+	0.861371i	$0.330393\pi$
$710$	4.25285	−	7.36615i	0.159607	−	0.276447i
$711$	−5.46053	−	33.3886i	−0.204786	−	1.25217i
$712$	−5.78461	+	3.33975i	−0.216788	+	0.125162i
$713$	−7.43889	+	12.8845i	−0.278589	+	0.482530i
$714$	7.94122	−	15.4576i	0.297193	−	0.578485i
$715$	0.355403	+	0.615575i	0.0132913	+	0.0230212i
$716$	−12.6316	−	7.29284i	−0.472064	−	0.272546i
$717$	4.72469	−	25.8549i	0.176447	−	0.965568i
$718$	−9.93362	−	17.2055i	−0.370719	−	0.642105i
$719$	−4.20805	−	7.28856i	−0.156934	−	0.271817i	0.776828	−	0.629713i	$-0.216828\pi$
$719$	−4.20805	−	7.28856i	−0.156934	−	0.271817i	−0.933761	+	0.357896i	$0.883494\pi$
$720$	13.7531	+	5.20011i	0.512549	+	0.193797i
$721$	−33.9637	+	7.94384i	−1.26488	+	0.295844i
$722$	−66.5933	−	38.4476i	−2.47835	−	1.43087i
$723$	−3.01505	+	16.4992i	−0.112131	+	0.613612i
$724$		−	22.7493i		−	0.845469i
$725$		−	7.94684i		−	0.295138i
$726$	32.4363	−	11.5782i	1.20382	−	0.429707i
$727$	33.6074	+	19.4032i	1.24643	+	0.719626i	0.970395	−	0.241522i	$-0.0776466\pi$
$727$	33.6074	+	19.4032i	1.24643	+	0.719626i	0.276034	+	0.961148i	$0.410980\pi$
$728$	−8.05141	−	2.43633i	−0.298405	−	0.0902963i
$729$	12.6194	+	23.8695i	0.467384	+	0.884055i
$730$	1.08880	+	1.88586i	0.0402984	+	0.0697988i
$731$	2.75319	+	4.76867i	0.101830	+	0.176376i
$732$	−5.90678	−	5.01923i	−0.218321	−	0.185516i
$733$	34.4644	+	19.8980i	1.27297	+	0.734950i	0.975546	−	0.219795i	$-0.0705389\pi$
$733$	34.4644	+	19.8980i	1.27297	+	0.734950i	0.297425	+	0.954745i	$0.403872\pi$
$734$	4.25729	+	7.37385i	0.157140	+	0.272174i
$735$	−11.6563	+	3.33640i	−0.429948	+	0.123065i
$736$	−5.77357	+	10.0001i	−0.212816	+	0.368609i
$737$	−2.89227	+	1.66985i	−0.106538	+	0.0615097i
$738$	−19.2113	−	23.4815i	−0.707179	−	0.864367i
$739$	−8.38375	+	14.5211i	−0.308401	+	0.534167i	−0.978013	−	0.208545i	$-0.933127\pi$
$739$	−8.38375	+	14.5211i	−0.308401	+	0.534167i	0.669612	+	0.742712i	$0.266461\pi$
$740$	1.35841			0.0499361
$741$	11.6073	+	32.5178i	0.426404	+	1.19457i
$742$	−7.81745	−	33.4233i	−0.286988	−	1.22701i
$743$	29.7811	−	17.1941i	1.09256	−	0.630790i	0.158304	−	0.987390i	$-0.449397\pi$
$743$	29.7811	−	17.1941i	1.09256	−	0.630790i	0.934257	+	0.356600i	$0.116064\pi$
$744$	11.5910	−	13.6406i	0.424945	−	0.500088i
$745$	−9.81185	+	5.66487i	−0.359478	+	0.207545i
$746$	−49.6201	−	28.6482i	−1.81672	−	1.04888i
$747$	−43.2654	−	16.3588i	−1.58300	−	0.598537i
$748$			0.763983i			0.0279340i
$749$	5.37941	−	17.7775i	0.196559	−	0.649577i
$750$	2.40293	+	2.04187i	0.0877427	+	0.0745585i
$751$	9.74499	−	16.8788i	0.355600	−	0.615917i	−0.631621	−	0.775278i	$-0.717610\pi$
$751$	9.74499	−	16.8788i	0.355600	−	0.615917i	0.987220	+	0.159361i	$0.0509433\pi$
$752$	−43.9802			−1.60379
$753$	31.5143	−	37.0870i	1.14845	−	1.35152i
$754$			36.8548i			1.34217i
$755$	−18.0711			−0.657676
$756$	−17.6693	+	3.78689i	−0.642625	+	0.137728i
$757$	−11.6307			−0.422726			−0.211363	−	0.977408i	$-0.567790\pi$
$757$	−11.6307			−0.422726			−0.211363	+	0.977408i	$0.567790\pi$
$758$			13.3105i			0.483459i
$759$	0.562307	−	0.661739i	0.0204104	−	0.0240196i
$760$	−9.76699			−0.354286
$761$	9.22839	−	15.9840i	0.334529	−	0.579421i	−0.648865	−	0.760903i	$-0.724756\pi$
$761$	9.22839	−	15.9840i	0.334529	−	0.579421i	0.983394	+	0.181482i	$0.0580895\pi$
$762$	35.0477	+	29.7814i	1.26964	+	1.07887i
$763$	−6.15851	−	26.3306i	−0.222953	−	0.953231i
$764$		−	14.2719i		−	0.516338i
$765$	−4.83653	+	3.95699i	−0.174865	+	0.143065i
$766$	54.0826	+	31.2246i	1.95408	+	1.12819i
$767$	−4.76033	+	2.74838i	−0.171886	+	0.0992383i
$768$	23.4468	−	27.5929i	0.846064	−	0.995674i
$769$	15.1013	−	8.71871i	0.544565	−	0.314405i	−0.202362	−	0.979311i	$-0.564862\pi$
$769$	15.1013	−	8.71871i	0.544565	−	0.314405i	0.746927	+	0.664906i	$0.231528\pi$
$770$	0.980329	−	0.919444i	0.0353286	−	0.0331345i
$771$	−4.73863	−	13.2753i	−0.170658	−	0.478098i
$772$	8.25911			0.297252
$773$	15.6712	−	27.1434i	0.563655	−	0.976279i	−0.433519	−	0.901145i	$-0.642728\pi$
$773$	15.6712	−	27.1434i	0.563655	−	0.976279i	0.997173	−	0.0751342i	$-0.0239385\pi$
$774$	5.10621	−	13.5048i	0.183539	−	0.485420i
$775$	7.17091	−	4.14013i	0.257587	−	0.148718i
$776$	5.50380	−	9.53286i	0.197575	−	0.342210i
$777$	3.98044	−	2.56605i	0.142798	−	0.0920566i
$778$	25.7395	+	44.5821i	0.922806	+	1.59835i
$779$	37.6456	+	21.7347i	1.34879	+	0.778726i
$780$	−4.41948	−	3.75541i	−0.158243	−	0.134465i
$781$	0.651825	+	1.12899i	0.0233241	+	0.0403986i
$782$	−3.40689	−	5.90090i	−0.121830	−	0.211016i
$783$	−19.9765	−	36.1393i	−0.713903	−	1.29151i
$784$	−2.19679	+	34.2375i	−0.0784566	+	1.22277i
$785$	17.7971	+	10.2752i	0.635206	+	0.366736i
$786$	9.83332	−	3.51002i	0.350743	−	0.125198i
$787$			0.210222i			0.00749360i	0.999993	+	0.00374680i	$0.00119265\pi$
$787$			0.210222i			0.00749360i	−0.999993	+	0.00374680i	$0.998807\pi$
$788$			26.4024i			0.940545i
$789$	−0.159635	+	0.873567i	−0.00568314	+	0.0310998i
$790$	−17.7805	−	10.2656i	−0.632602	−	0.365233i
$791$	8.82413	−	29.1614i	0.313750	−	1.03686i
$792$	−0.808639	+	0.661585i	−0.0287337	+	0.0235084i
$793$	−4.33650	−	7.51104i	−0.153994	−	0.266725i
$794$	4.05264	+	7.01938i	0.143823	+	0.249108i
$795$	−2.21881	+	12.1420i	−0.0786931	+	0.430631i
$796$	−25.4111	−	14.6711i	−0.900674	−	0.520004i
$797$	14.9432	+	25.8824i	0.529315	+	0.916801i	0.999415	+	0.0341878i	$0.0108844\pi$
$797$	14.9432	+	25.8824i	0.529315	+	0.916801i	−0.470100	+	0.882613i	$0.655782\pi$
$798$	54.8723	−	35.3742i	1.94246	−	1.25223i
$799$	9.34587	−	16.1875i	0.330633	−	0.572673i
$800$	5.56558	−	3.21329i	0.196773	−	0.113607i
$801$	−12.4262	+	10.1664i	−0.439056	+	0.359213i
$802$	−13.3410	+	23.1072i	−0.471086	+	0.815945i
$803$	−0.333757			−0.0117780
$804$	17.6447	−	20.7648i	0.622280	−	0.732318i
$805$	−1.37684	+	4.55008i	−0.0485271	+	0.160369i
$806$	−33.2563	+	19.2005i	−1.17140	+	0.676310i
$807$	−0.217898	−	0.610440i	−0.00767036	−	0.0214885i
$808$	−19.7482	+	11.4016i	−0.694739	+	0.401107i
$809$	−6.84767	−	3.95351i	−0.240751	−	0.138998i	0.374771	−	0.927118i	$-0.377721\pi$
$809$	−6.84767	−	3.95351i	−0.240751	−	0.138998i	−0.615522	+	0.788120i	$0.711055\pi$
$810$	16.0604	+	3.24524i	0.564306	+	0.114026i
$811$		−	48.2315i		−	1.69364i	−0.531883	−	0.846818i	$-0.678515\pi$
$811$		−	48.2315i		−	1.69364i	0.531883	−	0.846818i	$-0.321485\pi$
$812$	26.9102	−	6.29408i	0.944363	−	0.220879i
$813$	−2.02230	+	11.0666i	−0.0709251	+	0.388123i
$814$	−0.262495	+	0.454655i	−0.00920046	+	0.0159357i
$815$	−0.773548			−0.0270962
$816$	5.94447	+	16.6534i	0.208098	+	0.582987i
$817$			20.6864i			0.723726i
$818$	24.1607			0.844759
$819$	−20.0441	−	2.65573i	−0.700397	−	0.0927988i
$820$	−7.30155			−0.254981
$821$		−	16.6177i		−	0.579962i	−0.957032	−	0.289981i	$-0.906351\pi$
$821$		−	16.6177i		−	0.579962i	0.957032	−	0.289981i	$-0.0936490\pi$
$822$	29.7324	+	5.43326i	1.03704	+	0.189507i
$823$	−46.8777			−1.63406			−0.817028	−	0.576599i	$-0.804380\pi$
$823$	−46.8777			−1.63406			−0.817028	+	0.576599i	$0.804380\pi$
$824$	8.22725	−	14.2500i	0.286610	−	0.496423i
$825$	−0.455171	+	0.162474i	−0.0158470	+	0.00565662i
$826$	7.11020	+	7.58103i	0.247395	+	0.263778i
$827$		−	22.0393i		−	0.766381i	−0.923669	−	0.383191i	$-0.874825\pi$
$827$		−	22.0393i		−	0.766381i	0.923669	−	0.383191i	$-0.125175\pi$
$828$	−2.50582	+	6.62734i	−0.0870833	+	0.230316i
$829$	−35.2039	−	20.3250i	−1.22268	−	0.705915i	−0.257192	−	0.966360i	$-0.582797\pi$
$829$	−35.2039	−	20.3250i	−1.22268	−	0.705915i	−0.965489	+	0.260445i	$0.916131\pi$
$830$	−24.3092	+	14.0349i	−0.843785	+	0.487159i
$831$	6.21525	+	1.13577i	0.215605	+	0.0393994i
$832$	−4.18653	+	2.41709i	−0.145142	+	0.0837976i
$833$	−12.1348	−	8.08408i	−0.420445	−	0.280097i
$834$	−5.49962	−	1.00499i	−0.190436	−	0.0348001i
$835$	−9.80797			−0.339419
$836$	−1.43507	+	2.48561i	−0.0496329	+	0.0859667i
$837$	22.2033	−	36.8538i	0.767459	−	1.27385i
$838$	−59.4620	+	34.3304i	−2.05408	+	1.18592i
$839$	−21.5312	+	37.2932i	−0.743341	+	1.28750i	0.207625	+	0.978209i	$0.433427\pi$
$839$	−21.5312	+	37.2932i	−0.743341	+	1.28750i	−0.950966	+	0.309296i	$0.899907\pi$
$840$	2.61365	−	5.08746i	0.0901794	−	0.175534i
$841$	17.0761	+	29.5767i	0.588831	+	1.01989i
$842$	−53.7497	−	31.0324i	−1.85234	−	1.06945i
$843$	−5.37729	+	1.91943i	−0.185204	+	0.0661087i
$844$	0.335624	+	0.581318i	0.0115527	+	0.0200098i
$845$	3.25541	+	5.63854i	0.111990	+	0.193972i
$846$	−48.3677	+	7.91028i	−1.66292	+	0.271961i
$847$	−6.58122	−	28.1379i	−0.226134	−	0.966829i
$848$	30.2474	+	17.4633i	1.03870	+	0.599694i
$849$	−18.4036	−	15.6382i	−0.631609	−	0.536703i
$850$			3.79222i			0.130072i
$851$		−	1.85689i		−	0.0636532i
$852$	−8.10553	−	6.88759i	−0.277691	−	0.235965i
$853$	29.0793	+	16.7889i	0.995655	+	0.574842i	0.906960	−	0.421217i	$-0.138397\pi$
$853$	29.0793	+	16.7889i	0.995655	+	0.574842i	0.0886951	+	0.996059i	$0.471730\pi$
$854$	−11.9616	+	11.2187i	−0.409319	+	0.383897i
$855$	−23.1685	+	3.78908i	−0.792345	+	0.129584i
$856$	4.38097	+	7.58806i	0.149738	+	0.259354i
$857$	2.90499	+	5.03158i	0.0992324	+	0.171876i	0.911367	−	0.411594i	$-0.135028\pi$
$857$	2.90499	+	5.03158i	0.0992324	+	0.171876i	−0.812135	+	0.583470i	$0.801695\pi$
$858$	2.11093	−	0.753500i	0.0720660	−	0.0257241i
$859$	−26.7041	−	15.4176i	−0.911134	−	0.526043i	−0.0303380	−	0.999540i	$-0.509658\pi$
$859$	−26.7041	−	15.4176i	−0.911134	−	0.526043i	−0.880796	+	0.473496i	$0.842992\pi$
$860$	−1.73735	−	3.00918i	−0.0592431	−	0.102612i
$861$	−21.3952	+	13.7927i	−0.729146	+	0.470055i
$862$	25.1387	−	43.5415i	0.856228	−	1.48303i
$863$	−28.8588	+	16.6616i	−0.982365	+	0.567169i	−0.902983	−	0.429676i	$-0.858628\pi$
$863$	−28.8588	+	16.6616i	−0.982365	+	0.567169i	−0.0793816	+	0.996844i	$0.525295\pi$
$864$	17.2327	−	28.6035i	0.586269	−	0.973109i
$865$	−1.48675	+	2.57513i	−0.0505511	+	0.0875570i
$866$	−13.3987			−0.455305
$867$	21.5725	+	3.94213i	0.732640	+	0.133882i
$868$	19.6992	+	21.0036i	0.668633	+	0.712910i
$869$	2.72518	−	1.57338i	0.0924454	−	0.0533734i
$870$	−24.6506	−	4.50462i	−0.835732	−	0.152721i
$871$	26.4044	−	15.2446i	0.894681	−	0.516544i
$872$	11.0474	+	6.37823i	0.374113	+	0.215994i
$873$	9.35742	−	24.7483i	0.316701	−	0.837602i
$874$		−	25.5980i		−	0.865867i
$875$	1.92980	−	1.80994i	0.0652390	−	0.0611872i
$876$	2.56468	−	0.915465i	0.0866524	−	0.0309307i
$877$	3.52428	−	6.10424i	0.119007	−	0.206125i	−0.800368	−	0.599509i	$-0.795362\pi$
$877$	3.52428	−	6.10424i	0.119007	−	0.206125i	0.919374	+	0.393384i	$0.128696\pi$
$878$	8.22112			0.277449
$879$	−49.2586	−	9.00146i	−1.66145	−	0.303612i
$880$			1.36758i			0.0461011i
$881$	−49.3816			−1.66371			−0.831855	−	0.554993i	$-0.812721\pi$
$881$	−49.3816			−1.66371			−0.831855	+	0.554993i	$0.812721\pi$
$882$	3.74202	+	38.0482i	0.126000	+	1.28115i
$883$	42.7741			1.43946			0.719732	−	0.694252i	$-0.244265\pi$
$883$	42.7741			1.43946			0.719732	+	0.694252i	$0.244265\pi$
$884$		−	6.97465i		−	0.234583i
$885$	−1.25644	−	3.51990i	−0.0422346	−	0.118320i
$886$	57.6151			1.93562
$887$	10.0690	−	17.4400i	0.338084	−	0.585579i	−0.645988	−	0.763347i	$-0.723554\pi$
$887$	10.0690	−	17.4400i	0.338084	−	0.585579i	0.984072	+	0.177769i	$0.0568878\pi$
$888$	−0.401608	+	2.19772i	−0.0134771	+	0.0737505i
$889$	28.1468	−	26.3987i	0.944013	−	0.885383i
$890$			9.74307i			0.326588i
$891$	−1.66153	+	1.88307i	−0.0556633	+	0.0630852i
$892$	−20.4153	−	11.7868i	−0.683554	−	0.394650i
$893$	60.8134	−	35.1106i	2.03504	−	1.17493i
$894$	12.0103	+	33.6468i	0.401684	+	1.12532i
$895$	9.60988	−	5.54827i	0.321223	−	0.185458i
$896$	−17.0103	−	18.1367i	−0.568275	−	0.605906i
$897$	−5.13348	+	6.04124i	−0.171402	+	0.201711i
$898$	−60.4363			−2.01679
$899$	−32.9009	+	56.9860i	−1.09731	+	1.90059i
$900$	3.05200	−	2.49699i	0.101733	−	0.0832329i
$901$	−12.8552	+	7.42198i	−0.428270	+	0.247262i
$902$	1.41093	−	2.44381i	0.0469790	−	0.0813699i
$903$	−10.7752	−	5.53569i	−0.358576	−	0.184216i
$904$	7.18633	+	12.4471i	0.239014	+	0.413984i
$905$	14.9885	+	8.65362i	0.498235	+	0.287656i
$906$	−10.2435	+	56.0555i	−0.340318	+	1.86232i
$907$	−6.62978	−	11.4831i	−0.220138	−	0.381291i	0.734711	−	0.678380i	$-0.237318\pi$
$907$	−6.62978	−	11.4831i	−0.220138	−	0.381291i	−0.954850	+	0.297089i	$0.903984\pi$
$908$	−7.27110	−	12.5939i	−0.241300	−	0.417944i
$909$	−42.4218	+	34.7073i	−1.40704	+	1.15117i
$910$	−8.94975	+	8.39391i	−0.296681	+	0.278255i
$911$	35.4901	+	20.4902i	1.17584	+	0.678871i	0.955048	−	0.296450i	$-0.0958029\pi$
$911$	35.4901	+	20.4902i	1.17584	+	0.678871i	0.220791	+	0.975321i	$0.429136\pi$
$912$	−11.9416	+	65.3479i	−0.395426	+	2.16389i
$913$		−	4.30221i		−	0.142382i
$914$		−	14.6841i		−	0.485705i
$915$	5.55384	−	1.98245i	0.183604	−	0.0655378i
$916$	30.4102	+	17.5573i	1.00478	+	0.580111i
$917$	−1.99515	−	8.53022i	−0.0658856	−	0.281693i
$918$	9.53277	+	17.2456i	0.314628	+	0.569190i
$919$	17.2002	+	29.7915i	0.567381	+	0.982732i	0.996824	+	0.0796385i	$0.0253766\pi$
$919$	17.2002	+	29.7915i	0.567381	+	0.982732i	−0.429443	+	0.903094i	$0.641290\pi$
$920$	−1.12129	−	1.94213i	−0.0369678	−	0.0640301i
$921$	−12.6983	−	10.7903i	−0.418424	−	0.355552i
$922$	22.8564	+	13.1961i	0.752735	+	0.434592i
$923$	−5.95073	−	10.3070i	−0.195871	−	0.339258i
$924$	−0.910689	−	1.41265i	−0.0299595	−	0.0464729i
$925$	−0.516727	+	0.894997i	−0.0169899	+	0.0294273i
$926$	−64.4301	+	37.1988i	−2.11731	+	1.22243i
$927$	13.9878	−	36.9945i	0.459418	−	1.21506i
$928$	−25.5355	+	44.2287i	−0.838243	+	1.45188i
$929$	−19.2085			−0.630211			−0.315105	−	0.949057i	$-0.602040\pi$
$929$	−19.2085			−0.630211			−0.315105	+	0.949057i	$0.602040\pi$
$930$	−8.77761	−	24.5905i	−0.287829	−	0.806354i
$931$	−24.2952	−	49.0955i	−0.796242	−	1.60904i
$932$	0.00537225	−	0.00310167i	0.000175974	−	0.000101599i
$933$	−3.43079	+	4.03746i	−0.112319	+	0.132180i
$934$	19.1730	−	11.0695i	0.627360	−	0.362206i
$935$	−0.503356	−	0.290613i	−0.0164615	−	0.00950405i
$936$	7.38233	−	6.03983i	0.241299	−	0.197418i
$937$		−	1.73959i		−	0.0568300i	−0.999596	−	0.0284150i	$-0.990954\pi$
$937$		−	1.73959i		−	0.0568300i	0.999596	−	0.0284150i	$-0.00904599\pi$
$938$	−39.4386	−	42.0502i	−1.28771	−	1.37299i
$939$	−4.53783	−	3.85598i	−0.148087	−	0.125835i
$940$	−5.89753	+	10.2148i	−0.192356	+	0.333171i
$941$	3.51509			0.114589			0.0572944	−	0.998357i	$-0.481753\pi$
$941$	3.51509			0.114589			0.0572944	+	0.998357i	$0.481753\pi$
$942$	41.9610	−	49.3810i	1.36716	−	1.60892i
$943$			9.98091i			0.325023i
$944$	−10.5757			−0.344209
$945$	4.22621	−	13.0820i	0.137479	−	0.425558i
$946$	1.34288			0.0436609
$947$			6.10408i			0.198356i	0.995070	+	0.0991780i	$0.0316213\pi$
$947$			6.10408i			0.198356i	−0.995070	+	0.0991780i	$0.968379\pi$
$948$	−16.6254	+	19.5652i	−0.539966	+	0.635448i
$949$	3.04698			0.0989090
$950$	−7.12332	+	12.3380i	−0.231111	+	0.400296i
$951$	−6.78607	−	5.76640i	−0.220053	−	0.186988i
$952$	6.69769	−	1.56654i	0.217073	−	0.0507717i
$953$		−	0.788320i		−	0.0255362i	−0.999918	−	0.0127681i	$-0.995936\pi$
$953$		−	0.788320i		−	0.0255362i	0.999918	−	0.0127681i	$-0.00406432\pi$
$954$	36.4059	+	13.7652i	1.17868	+	0.445665i
$955$	9.40312	+	5.42889i	0.304278	+	0.175675i
$956$	−17.2737	+	9.97296i	−0.558671	+	0.322549i
$957$	2.48698	−	2.92676i	0.0803928	−	0.0946087i
$958$	−37.4436	+	21.6181i	−1.20975	+	0.698449i
$959$	7.34488	−	24.2729i	0.237179	−	0.783812i
$960$	−1.10499	−	3.09562i	−0.0356632	−	0.0999106i
$961$	−37.5626			−1.21170
$962$	2.39641	−	4.15070i	0.0772632	−	0.133824i
$963$	13.3359	+	16.3002i	0.429745	+	0.525266i
$964$	11.0231	−	6.36422i	0.355032	−	0.204978i
$965$	−3.14169	+	5.44157i	−0.101135	+	0.175170i
$966$	13.3336	+	6.85004i	0.429001	+	0.220396i
$967$	−9.70715	−	16.8133i	−0.312161	−	0.540679i	0.666669	−	0.745354i	$-0.267719\pi$
$967$	−9.70715	−	16.8133i	−0.312161	−	0.540679i	−0.978830	+	0.204675i	$0.934386\pi$
$968$	11.8057	+	6.81602i	0.379449	+	0.219075i
$969$	−21.5146	−	18.2818i	−0.691148	−	0.587296i
$970$	−8.02813	−	13.9051i	−0.257768	−	0.446467i
$971$	18.5702	+	32.1645i	0.595945	+	1.03221i	0.993413	+	0.114591i	$0.0365556\pi$
$971$	18.5702	+	32.1645i	0.595945	+	1.03221i	−0.397468	+	0.917616i	$0.630111\pi$
$972$	7.60253	−	19.0274i	0.243851	−	0.610305i
$973$	−1.35859	+	4.48977i	−0.0435543	+	0.143935i
$974$	46.3720	+	26.7729i	1.48586	+	0.857859i
$975$	4.15541	−	1.48328i	0.133080	−	0.0475029i
$976$		−	16.6867i		−	0.534129i
$977$		−	45.1618i		−	1.44486i	−0.691446	−	0.722428i	$-0.743026\pi$
$977$		−	45.1618i		−	1.44486i	0.691446	−	0.722428i	$-0.256974\pi$
$978$	−0.438481	+	2.39949i	−0.0140211	+	0.0767274i
$979$	−1.29323	−	0.746650i	−0.0413320	−	0.0238630i
$980$	7.65741	+	5.10131i	0.244607	+	0.162955i
$981$	28.6802	+	10.8441i	0.915689	+	0.346225i
$982$	25.8193	+	44.7203i	0.823926	+	1.42708i
$983$	−14.8568	−	25.7326i	−0.473857	−	0.820744i	0.525695	−	0.850673i	$-0.323805\pi$
$983$	−14.8568	−	25.7326i	−0.473857	−	0.820744i	−0.999552	+	0.0299290i	$0.990472\pi$
$984$	2.15868	−	11.8129i	0.0688161	−	0.376582i
$985$	−17.3954	−	10.0432i	−0.554263	−	0.320004i
$986$	−15.0681	−	26.0987i	−0.479865	−	0.831151i
$987$	2.01486	+	41.0723i	0.0641337	+	1.30734i
$988$	13.1012	−	22.6920i	0.416805	−	0.721928i
$989$	−4.11342	+	2.37488i	−0.130799	+	0.0755169i
$990$	0.245973	+	1.50401i	0.00781753	+	0.0478005i
$991$	−7.42230	+	12.8558i	−0.235777	+	0.408378i	−0.959498	−	0.281714i	$-0.909097\pi$
$991$	−7.42230	+	12.8558i	−0.235777	+	0.408378i	0.723721	+	0.690093i	$0.242430\pi$
$992$	−53.2137			−1.68954
$993$	12.8979	−	15.1787i	0.409303	−	0.481680i
$994$	−16.4143	+	15.3948i	−0.520629	+	0.488294i
$995$	19.3323	−	11.1615i	0.612877	−	0.353844i
$996$	11.8006	+	33.0593i	0.373915	+	1.04752i
$997$	−34.5547	+	19.9502i	−1.09436	+	0.631828i	−0.934734	−	0.355349i	$-0.884362\pi$
$997$	−34.5547	+	19.9502i	−1.09436	+	0.631828i	−0.159625	+	0.987178i	$0.551029\pi$
$998$	−52.6118	−	30.3755i	−1.66540	−	0.961518i
$999$	−0.100063	+	5.36905i	−0.00316587	+	0.169869i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	315.2.t.b.101.3	✓	30
3.2	odd	2		945.2.t.b.521.13		30
7.5	odd	6		315.2.be.b.236.3	yes	30
9.4	even	3		945.2.be.b.206.13		30
9.5	odd	6		315.2.be.b.311.3	yes	30
21.5	even	6		945.2.be.b.656.13		30
63.5	even	6	inner	315.2.t.b.131.13	yes	30
63.40	odd	6		945.2.t.b.341.3		30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
315.2.t.b.101.3	✓	30	1.1	even	1	trivial
315.2.t.b.131.13	yes	30	63.5	even	6	inner
315.2.be.b.236.3	yes	30	7.5	odd	6
315.2.be.b.311.3	yes	30	9.5	odd	6
945.2.t.b.341.3		30	63.40	odd	6
945.2.t.b.521.13		30	3.2	odd	2
945.2.be.b.206.13		30	9.4	even	3
945.2.be.b.656.13		30	21.5	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 315 = 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	315.t (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-1.82056i q^{2} +(1.12156 - 1.31989i) q^{3} -1.31444 q^{4} +(0.500000 - 0.866025i) q^{5} +(-2.40293 - 2.04187i) q^{6} +(-1.92980 + 1.80994i) q^{7} -1.24811i q^{8} +(-0.484202 - 2.96067i) q^{9} +O(q^{10})\)	\(q-1.82056i q^{2} +(1.12156 - 1.31989i) q^{3} -1.31444 q^{4} +(0.500000 - 0.866025i) q^{5} +(-2.40293 - 2.04187i) q^{6} +(-1.92980 + 1.80994i) q^{7} -1.24811i q^{8} +(-0.484202 - 2.96067i) q^{9} +(-1.57665 - 0.910280i) q^{10} +(0.241650 - 0.139517i) q^{11} +(-1.47422 + 1.73491i) q^{12} +(-2.20610 + 1.27369i) q^{13} +(3.29511 + 3.51331i) q^{14} +(-0.582275 - 1.63124i) q^{15} -4.90113 q^{16} +(1.04150 - 1.80393i) q^{17} +(-5.39007 + 0.881518i) q^{18} +(6.77701 - 3.91271i) q^{19} +(-0.657218 + 1.13833i) q^{20} +(0.224535 + 4.57707i) q^{21} +(-0.253998 - 0.439938i) q^{22} +(1.55606 + 0.898389i) q^{23} +(-1.64736 - 1.39983i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(2.31883 + 4.01634i) q^{26} +(-4.45081 - 2.68148i) q^{27} +(2.53659 - 2.37905i) q^{28} +(6.88216 + 3.97342i) q^{29} +(-2.96978 + 1.06007i) q^{30} +8.28025i q^{31} +6.42658i q^{32} +(0.0868790 - 0.475427i) q^{33} +(-3.28416 - 1.89611i) q^{34} +(0.602558 + 2.57622i) q^{35} +(0.636452 + 3.89161i) q^{36} +(-0.516727 - 0.894997i) q^{37} +(-7.12332 - 12.3380i) q^{38} +(-0.793147 + 4.34033i) q^{39} +(-1.08090 - 0.624055i) q^{40} +(2.77745 + 4.81068i) q^{41} +(8.33283 - 0.408779i) q^{42} +(-1.32175 + 2.28933i) q^{43} +(-0.317633 + 0.183386i) q^{44} +(-2.80611 - 1.06100i) q^{45} +(1.63557 - 2.83289i) q^{46} +8.97348 q^{47} +(-5.49692 + 6.46894i) q^{48} +(0.448220 - 6.98564i) q^{49} +(-1.57665 + 0.910280i) q^{50} +(-1.21288 - 3.39787i) q^{51} +(2.89978 - 1.67419i) q^{52} +(-6.17152 - 3.56313i) q^{53} +(-4.88179 + 8.10296i) q^{54} -0.279033i q^{55} +(2.25901 + 2.40860i) q^{56} +(2.43650 - 13.3332i) q^{57} +(7.23384 - 12.5294i) q^{58} +2.15780 q^{59} +(0.765363 + 2.14417i) q^{60} +3.40467i q^{61} +15.0747 q^{62} +(6.29305 + 4.83710i) q^{63} +1.89770 q^{64} +2.54739i q^{65} +(-0.865543 - 0.158168i) q^{66} -11.9688 q^{67} +(-1.36898 + 2.37115i) q^{68} +(2.93098 - 1.04622i) q^{69} +(4.69017 - 1.09699i) q^{70} +4.67203i q^{71} +(-3.69524 + 0.604337i) q^{72} +(-1.03587 - 0.598059i) q^{73} +(-1.62939 + 0.940732i) q^{74} +(-1.70384 - 0.311357i) q^{75} +(-8.90795 + 5.14301i) q^{76} +(-0.213818 + 0.706611i) q^{77} +(7.90182 + 1.44397i) q^{78} +11.2774 q^{79} +(-2.45057 + 4.24450i) q^{80} +(-8.53110 + 2.86712i) q^{81} +(8.75813 - 5.05651i) q^{82} +(7.70913 - 13.3526i) q^{83} +(-0.295137 - 6.01627i) q^{84} +(-1.04150 - 1.80393i) q^{85} +(4.16786 + 2.40632i) q^{86} +(12.9632 - 4.62724i) q^{87} +(-0.174132 - 0.301606i) q^{88} +(-2.67584 - 4.63470i) q^{89} +(-1.93162 + 5.10870i) q^{90} +(1.95201 - 6.45088i) q^{91} +(-2.04533 - 1.18087i) q^{92} +(10.9290 + 9.28681i) q^{93} -16.3368i q^{94} -7.82542i q^{95} +(8.48235 + 7.20780i) q^{96} +(7.63783 + 4.40971i) q^{97} +(-12.7178 - 0.816012i) q^{98} +(-0.530069 - 0.647891i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q + 4 q^{3} - 30 q^{4} + 15 q^{5} - q^{6} - 3 q^{7} - 2 q^{9}+O(q^{10}) \) 30 * q + 4 * q^3 - 30 * q^4 + 15 * q^5 - q^6 - 3 * q^7 - 2 * q^9	\( 30 q + 4 q^{3} - 30 q^{4} + 15 q^{5} - q^{6} - 3 q^{7} - 2 q^{9} + 3 q^{10} + 9 q^{11} + 15 q^{12} - 12 q^{13} - 27 q^{14} - q^{15} + 42 q^{16} - 3 q^{17} - 4 q^{18} - 15 q^{20} + 4 q^{21} + 15 q^{22} + q^{24} - 15 q^{25} + 24 q^{26} - 5 q^{27} + 27 q^{28} - 2 q^{30} - 25 q^{33} + 48 q^{34} - 6 q^{35} + 21 q^{36} - 3 q^{37} - 30 q^{38} - 3 q^{39} + 3 q^{40} - 18 q^{41} - 16 q^{42} + 12 q^{43} + 15 q^{44} - 7 q^{45} + 9 q^{46} - 60 q^{47} - 40 q^{48} - 15 q^{49} + 3 q^{50} - 48 q^{51} - 33 q^{52} - 30 q^{53} + 35 q^{54} + 42 q^{56} - 21 q^{57} + 30 q^{59} + 33 q^{60} + 12 q^{62} - 47 q^{63} - 138 q^{64} + 100 q^{66} + 12 q^{67} - 21 q^{68} + 32 q^{69} - 18 q^{70} + 85 q^{72} + 6 q^{73} + 54 q^{74} - 5 q^{75} - 54 q^{76} - 9 q^{77} - 18 q^{78} + 24 q^{79} + 21 q^{80} - 14 q^{81} + 6 q^{82} - 6 q^{83} - 9 q^{84} + 3 q^{85} - 60 q^{86} - 16 q^{87} - 48 q^{88} - 3 q^{89} + 22 q^{90} + 15 q^{91} - 3 q^{92} + 69 q^{93} - 48 q^{96} + 36 q^{97} + 24 q^{98} - q^{99}+O(q^{100}) \) 30 * q + 4 * q^3 - 30 * q^4 + 15 * q^5 - q^6 - 3 * q^7 - 2 * q^9 + 3 * q^10 + 9 * q^11 + 15 * q^12 - 12 * q^13 - 27 * q^14 - q^15 + 42 * q^16 - 3 * q^17 - 4 * q^18 - 15 * q^20 + 4 * q^21 + 15 * q^22 + q^24 - 15 * q^25 + 24 * q^26 - 5 * q^27 + 27 * q^28 - 2 * q^30 - 25 * q^33 + 48 * q^34 - 6 * q^35 + 21 * q^36 - 3 * q^37 - 30 * q^38 - 3 * q^39 + 3 * q^40 - 18 * q^41 - 16 * q^42 + 12 * q^43 + 15 * q^44 - 7 * q^45 + 9 * q^46 - 60 * q^47 - 40 * q^48 - 15 * q^49 + 3 * q^50 - 48 * q^51 - 33 * q^52 - 30 * q^53 + 35 * q^54 + 42 * q^56 - 21 * q^57 + 30 * q^59 + 33 * q^60 + 12 * q^62 - 47 * q^63 - 138 * q^64 + 100 * q^66 + 12 * q^67 - 21 * q^68 + 32 * q^69 - 18 * q^70 + 85 * q^72 + 6 * q^73 + 54 * q^74 - 5 * q^75 - 54 * q^76 - 9 * q^77 - 18 * q^78 + 24 * q^79 + 21 * q^80 - 14 * q^81 + 6 * q^82 - 6 * q^83 - 9 * q^84 + 3 * q^85 - 60 * q^86 - 16 * q^87 - 48 * q^88 - 3 * q^89 + 22 * q^90 + 15 * q^91 - 3 * q^92 + 69 * q^93 - 48 * q^96 + 36 * q^97 + 24 * q^98 - q^99

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